Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press (CUP)  

In high-Reynolds-number turbulence the spatial distribution of velocity fluctuation at small scales is strongly non-uniform. In accordance with the non-uniformity, the distributions of the inertial and viscous forces are also non-uniform. According to direct numerical simulation (DNS) of forced turbulence of an incompressible fluid obeying the Navier–Stokes equation in a periodic box at the Taylor microscale Reynolds number <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline1.png" />
<tex-math>$R_\lambda \approx 1100$</tex-math>
</alternatives>
</inline-formula>, the average <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline2.png" />
<tex-math>$\langle R_{loc}\rangle$</tex-math>
</alternatives>
</inline-formula> over the space of the ‘local Reynolds number’ <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline3.png" />
<tex-math>$R_ {loc}$</tex-math>
</alternatives>
</inline-formula>, which is defined as the ratio of inertial to viscous forces at each point in the flow, is much smaller than the conventional ‘Reynolds number’ given by <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline4.png" />
<tex-math>$Re \equiv UL/\nu$</tex-math>
</alternatives>
</inline-formula>, where <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline5.png" />
<tex-math>$U$</tex-math>
</alternatives>
</inline-formula> and <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline6.png" />
<tex-math>$L$</tex-math>
</alternatives>
</inline-formula> are the characteristic velocity and length of the energy-containing eddies, and <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline7.png" />
<tex-math>$\nu$</tex-math>
</alternatives>
</inline-formula> is the kinematic viscosity. While both conditional averages of the inertial and viscous forces for a given squared vorticity <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline8.png" />
<tex-math>$\omega ^{2}$</tex-math>
</alternatives>
</inline-formula> increase with <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline9.png" />
<tex-math>$\omega ^{2}$</tex-math>
</alternatives>
</inline-formula> at large <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline10.png" />
<tex-math>$\omega ^{2}$</tex-math>
</alternatives>
</inline-formula>, the conditional average of <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline11.png" />
<tex-math>$R_ {loc}$</tex-math>
</alternatives>
</inline-formula> is almost independent of <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline12.png" />
<tex-math>$\omega ^{2}$</tex-math>
</alternatives>
</inline-formula>. A comparison of the DNS field with a random structureless velocity field suggests that the increase in the conditional average of <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline13.png" />
<tex-math>$R_ {loc}$</tex-math>
</alternatives>
</inline-formula> with <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline14.png" />
<tex-math>$\omega ^{2}$</tex-math>
</alternatives>
</inline-formula> at large <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline15.png" />
<tex-math>$\omega ^{2}$</tex-math>
</alternatives>
</inline-formula> is suppressed by the Navier–Stokes dynamics. Something similar is also true for the conditional averages for a given local energy dissipation rate per unit mass. Certain features of intermittency effects such as that on the <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline16.png" />
<tex-math>$Re$</tex-math>
</alternatives>
</inline-formula> dependence of <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112021008065_inline17.png" />
<tex-math>$\langle R_{loc}\rangle$</tex-math>
</alternatives>
</inline-formula> are explained by a multi-fractal model by Dubrulle (<italic>J. Fluid Mech.</italic>, vol. 867, 2019, P1).

DOI： 10.1017/jfm.2021.806

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Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Astronomical Society  

Planetesimals are believed to be formed by the coagulation of dust grains in the protoplanetary disk turbulence. However, the bouncing and fragmentation barriers have not been completely solved, particularly for silicate dust. To circumvent these barriers, the turbulent clustering of dust particles must be properly treated. According to the minimum-mass solar nebula (MMSN) model, the Mach number of the turbulence ranges from Mrms ; 0.01–0.32, and thus the turbulence is often regarded as essentially incompressible. However, it has not been quantitatively investigated whether the incompressible limit is adequate for protoplanetary disk simulations. We therefore compare in this study the motions of inertial particles in direct numerical simulations (DNSs) of the Navier–Stokes equation between weakly compressible turbulence and incompressible turbulence. In the DNSs of compressible turbulence, we use an external force to set the total dissipation and the dilatational-to-solenoidal dissipation ratio. The DNSs reveal that despite the small Mach number Mrms(≾ 0.3), the compressible turbulence field notably differs from the incompressible field in terms of the density fluctuations, pressure fluctuations, and shocklet generation, depending on the ratio of the dilatational forcing. However, we quantitatively confirmed that these effects on the particle collision statistics are weak and that the motion of inertial particles in weakly compressible turbulence is dominated by the solenoidal velocity components. Therefore we can conclude that the incompressible assumption is appropriate for an investigation of the dust coagulation process in protoplanetary disk turbulence, as assumed in the MMSN model.

DOI： 10.3847/1538-4357/abe9ba

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Other Link： https://iopscience.iop.org/article/10.3847/1538-4357/abe9ba/pdf

Publishing type：Part of collection (book)  

Recent studies based on high-resolution direct numerical simulations (DNSs) of turbulence have shown that there are three different types of shear layers in homogeneous and inhomogeneous turbulent flows; at the outer edge (T/NT), in the interior (T/T) and within the buffer layer near the wall (T/W). All the layers play important roles in various turbulence phenomena in the fields of natural sciences and engineering applications. Data analyses showed that all the shear layers act as a barrier of the velocity fluctuations by blocking velocity fluctuations from the one side to the other side. It was suggested that the blocking mechanism of thin turbulent wall (T/W) layers can be used to control the turbulent wake of aerofoils. For high Reynolds number, flows over typical aerofoils at low angle of incidence in the thin turbulent boundary layers (TBLs) have a conditional structure with thin T/W layers which act as a barrier to eddies in the outer part of the TBL. Recent studies indicate that using disturbance—devices at the airfoil surface enhances the blocking effect of the TW barrier and leads—unexpectedly-to reduced shear fluctuations at the wall. This suggests that deeper understanding of the structures and properties of the T/W layers may provide ideas to consider the better strategies for aerofoils designs. In this paper, we review the recent studies on the three different types of shear layers, which are based on the high-resolution DNSs of homogeneous isotropic turbulence (HIT), turbulent boundary layer (TBL), and turbulent channel flow (TCF).

DOI： 10.1007/978-3-030-55594-8_43

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Publishing type：Part of collection (book)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-030-68049-7_4

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Authorship：Lead author   Publishing type：Research paper (international conference proceedings)  

Two-dimensional turbulent combustion with rapid temperature and pressure growth in the ignition process of a homogeneous n-heptane/air mixture is studied by high-resolution direct numerical simulations (DNSs) of the flow field of the mixture with up to 20482 grid points. The DNSs show that the turbulent flow mixes the temperature field so that it affects on the ignition delay. The DNSs show also that the rapid temperature and pressure growth due to the heat release at ignition makes drastic changes in the turbulent velocity field, especially in its compressible component, and causes pressure oscillations in some cases.

DOI： 10.1007/978-981-33-4960-5_32

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Royal Society  

Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation probability density function (PDF) based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers, these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume-weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds numbers, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.

DOI： 10.1098/rspa.2020.0591

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Other Link： https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2020.0591

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

We report results of a series of high-resolution direct numerical simulations (DNSs) of forced incompressible isotropic turbulence with the number of grid points and the Taylor scale Reynolds number Rλ up to 122883 and ∼2250, respectively. The DNSs show that there exists a scaling range (approximately 100<r/η<400), at which the second-order two-point velocity structure functions S2(r) fit well with a simple power-law, S2(r)/(ϵr)2/3=C2(r/L0)ζ, where r is the distance between the two points, η is the Kolmogorov length scale, ϵ is the mean rate of energy dissipation per unit mass, and L0 is the integral length scale. The exponent ζ is constant independent from Rλ. However, the coefficient C2 is dependent of Rλ or the viscosity. This implies that the power-law scaling range of 100<r/η<400 for Rλ up to ∼2250 is not the so-called "inertial subrange"in the sense that the statistics in the range are independent from the viscosity, as assumed in various turbulence theories. This suggests that the constancy of the scaling exponent of a structure function within a certain range does not necessarily mean that the exponent is the scaling exponent in "the inertial subrange."

DOI： 10.1103/physrevfluids.5.104608

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevFluids.5.104608/fulltext

Publishing type：Research paper (international conference proceedings)  

Direct numerical simulations of homogeneous isotropic turbulence at the Taylor microscale Reynolds number of order 103 show that the most energetic small scale motions and places with the most intense dissipation in the homogeneous isotropic turbulence are highly inhomogeneous and are located inside thin shear layers. We propose a local mechanism for how the most intense small scale and dissipative motions are produced in the vicinity of well separated thin shear layers. A model is developed based on a local rapid distortion analysis and the Townsend-Obukhov energy transfer hypothesis which is consistent with the data of the numerical simulation.

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Publishing type：Research paper (international conference proceedings)  

The time evolution of fine-scale tube-like vortical structures in isotropic turbulence is investigated by dynamic geometrical analysis. Our method successfully captures series of events like deformation, creation, extinction, merging and fission of the vortical structures. It is found that extinction and fission are more frequent than creation and merging, respectively.

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Publishing type：Research paper (international conference proceedings)  

It is shown for the first time how the degree of development in turbulence, i.e., if it is fully developed or if not how much developed, can be estimated by the multifractal theory called multifractal probability density function theory (MPDFT) [1]. Precise and self-consistent analyses of 40963 DNS turbulence [2] by means of MPDFT reveal that the turbulence with Rλ = 675 is in the fully developed turbulent state, but that the one with Rλ = 1132 is not fully developed yet. The degree of turbulence-development of the latter is estimated.

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Publishing type：Research paper (international conference proceedings)  

Data analysis of high resolution DNS of isotropic turbulence with the Taylor micro-scale Reynolds number Rλ = 1131 on 40963 grid points shows that there are significant thin shear layers of thickness of the order of Taylor micro-scale, consisting of a cluster of strong vortex tubes with typical diameter of order 10η (η is the Kolmogorov length scale). There are big velocity jumps of the order of the rms of the fluctuation velocity across the layers. The locally averaged energy dissipation rate in the layers is much greater than the mean energy dissipation rate, and contributes disproportionately to the overall mean dissipation rate. Up scale and down scale energy transfer to small eddies is largest within and just outside these layers (where the most intense vortices and dissipation occur). The statistics (based on a systematic study) of the layers will be presented and their Reynolds number dependence will be discussed.

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Publishing type：Research paper (international conference proceedings)  

A direct numerical simulation (DNS) code was developed for solving incompressible homogeneous isotropic turbulence with high Reynolds numbers in a periodic box using the Fourier spectral method. The code was parallelized using the Message Passing Interface and OpenMP with two-directional domain decomposition and optimized on the K computer. High resolution DNSs with up to grid points were performed on the K computer using the code. Efficiencies of 3.84%, 3.14%, and 2.24% peak performance were obtained in double precision DNSs with grid points, respectively. In addition, a two-path alias-free procedure is proposed and clarified its effectiveness for some number of parallel processes.

DOI： 10.1007/978-3-030-22747-0_44

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Language：English   Publishing type：Research paper (scientific journal)  

The position- and direction-dependence of length scales in turbulent channel flow was studied using the data from a series of direct numerical simulations (DNSs) of turbulent channel flow with the wall Reynolds number and the number of grid points ranging up to 5120 and 2048 × 1536 × 2048, respectively. According to the DNSs, there is a region of y in which the mean flow profile fits well with the log-law (log-law region), where y is the distance from the wall. The Taylor microscale is anisotropic, but has a simple y-dependence (∝ y1=2) in this region. The two-point fluctuating-velocity correlation at ∣r∣ ∼ y is also anisotropic and approximately depends on r through r=‘ðyÞ, where r is the displacement vector between two points, ‘ðyÞ is a function of only y, and ‘ðyÞ is close to, but not exactly equal to y.

DOI： 10.7566/JPSJ.88.064401

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Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Civil Engineers  

DOI： 10.2208/jscejam.75.2_i_509

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Authorship：Last author   Publishing type：Research paper (scientific journal)  

To quantitatively study the relationships between small-scale fluid motions and inertial particle clustering in turbulence, we track inertial particles in a turbulent flow through a direct numerical simulation of the forced incompressible Navier–Stokes equations. Further, we investigate the particle distribution in the eigenframe of the rate-of-strain tensor of the turbulent velocity field. The unconditional averages of the particle densities in the eigenframe demonstrate that the particle distribution exhibits specific patterns. In addition, the conditional averages in high-vorticity regions show that a strong vortex anisotropically generates low- and high-number-density regions depending on particle inertia.

DOI： 10.7566/JPSJ.87.093401

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

The coagulation of dust particles is a key process in planetesimal formation. However, the radial drift and bouncing barriers are not completely resolved, especially for silicate dust. Since the collision velocities of dust particles are regulated by turbulence in a protoplanetary disk, turbulent clustering should be properly treated. To that end, direct numerical simulations (DNSs) of the Navier-Stokes equations are requisite. In a series of papers, Pan & Padoan used a DNS with Reynolds number Re similar to 1000. Here, we perform DNSs with up to Re = 16,100, which allow us to track the motion of particles with Stokes numbers of 0.01 less than or similar to St less than or similar to 0.2 in the inertial range. Through the DNSs, we confirm that the rms relative velocity of particle pairs is smaller by more than a factor of two, compared to that by Ormel & Cuzzi. The distributions of the radial relative velocities are highly non-Gaussian. The results are almost consistent with those by Pan & Padoan or Pan et al. at low Re. Also, we find that the sticking rates for equal-sized particles are much higher than those for different-sized particles. Even in the strong-turbulence case with alpha-viscosity of 10(-2), the sticking rates are as high as greater than or similar to 50% and the bouncing probabilities are as low as similar to 10% for equal-sized particles of St less than or similar to 0.01. Thus, turbulent clustering plays a significant role in the growth of centimetersized compact aggregates (pebbles) and also enhances the solid abundance, which may lead to the streaming instability in a disk.

DOI： 10.3847/1538-4357/aaa976

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Language：English   Publishing type：Research paper (scientific journal)  

The scaling of turbulent motions is investigated by considering the flow in the eigenframe of the local strain-rate tensor. The flow patterns in this frame of reference are evaluated using existing direct numerical simulations of homogeneous isotropic turbulence over a Reynolds number range from Reλ=34:6 up to 1131, and also with reference to data for inhomogeneous, anisotropic wall turbulence. The average flow in the eigenframe reveals a shear layer structure containing tube-like vortices and a dissipation sheet, whose dimensions scale with the Kolmogorov length scale. The vorticity stretching motions scale with the Taylor length scale, λT , while the flow outside the shear layer scales with the integral length scale, L. Furthermore, the spatial organization of the vortices and the dissipation sheet defines a characteristic small-scale structure. The overall size of this characteristic small-scale structure is 120in all directions based on the coherence length of the vorticity. This is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Comparing the overall size of the characteristic small-scale structure with the largest flow scales and the vorticity stretching motions on the scale of 4λT shows that transitions in flow structure occur where Reλ∼45 and 250. Below these respective transitional Reynolds numbers, the small-scale motions and the vorticity stretching motions are progressively less well developed. Scale interactions are examined by decomposing the average shear layer into a local flow, which is induced by the shear layer vorticity, and a non-local flow, which represents the environment of the characteristic small-scale structure. The non-local strain is 4λT in width and height, which is consistent with observations in high Reynolds number flow of a 4λT wide instantaneous shear layer with many -scale vortical structures inside (Ishihara et al., Flow Turbul. Combust., vol. 91, 2013, pp. 895-929). In the average shear layer, vorticity aligns with the intermediate principal strain at small scales, while it aligns with the most stretching principal strain at larger scales, consistent with instantaneous turbulence. The length scale at which the alignment changes depends on the Reynolds number. When conditioning the flow in the eigenframe on extreme dissipation, the velocity is strongly affected over large distances. Moreover, the associated peak velocity remains Reynolds number dependent when normalized by the Kolmogorov velocity scale. It signifies that extreme dissipation is not simply a small-scale property, but is associated with large scales at the same time.

DOI： 10.1017/jfm.2017.538

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

We introduce boundary adaptedwavelets, which are orthogonal and have the same scale in the three spatial directions. The construction thus yields a multiresolution analysis. We analyse direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of 395, and investigate the role of coherent vorticity. Thresholding of the vorticity wavelet coefficients allows us to split the flow into two parts, coherent and incoherent flows. The coherent vorticity is reconstructed fromits few intensewavelet coefficients and the coherent velocity is reconstructed using Biot-Savart's law. The statistics of the coherent flow, i.e. energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets of the total flow are very well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e. noise-like, background flow whose energy is equidistributed.

DOI： 10.1080/14685248.2017.1284326

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A study is made about the energy spectrum E(k) of turbulence on the basis of highresolution direct numerical simulations (DNSs) of forced incompressible turbulence in a periodic box using a Fourier spectral method with the number of grid points and the Taylor scale Reynolds number R-lambda up to 12 288(3) and approximately 2300, respectively. The DNS data show that there is a wave-number range (approximately 5 x 10(-3) < k eta< 2 x 10(-2)) in which E(k) fits approximately well to Kolmogorov's k(-5/3) scaling, where eta is the Kolmogorov length scale. However, a close inspection shows that the exponent is a little smaller than -5/3, and E(k) in the range fits to E(k)/[<is an element of >(2/3)k(-5/3)] = c(kL)(m), where <is an element of > is the mean energy dissipation rate per unit mass; L is the integral length scale; and m approximate to -0.12. The coefficient c is independent of k, but has a R-lambda dependence, such as c = CR lambda zeta, where C approximate to 0.9 and zeta approximate to 0.14.

DOI： 10.1103/PhysRevFluids.1.082403

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

DOI： 10.1007/978-3-319-27386-0_17

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Recent large-scale direct numerical simulations (DNS) of high-Reynolds number (high-Re) turbulence, suggest that strong micro-scale tube-like vortices form clusters in localized thin regions of space. However, to this date no thorough quantitative and statistical analysis of the geometry of such vortical clusters has been conducted. This study is intended to generate new statistical tools to study the shape and dynamics of these intense vorticity and strain regions. We first propose a new method for locating and analysing the geometrical properties of thresholded vortical clusters contained inside boxes of a given size. Second, we use this new tool to investigate the natural presence of intense shear layers and their relevance as geometrical features of high-Re homogeneous turbulence. This new method is applied to the DNS of homogeneous incompressible turbulence with up to 40963 grid points, showing that the geometry of high vorticity regions varies strongly depending on the threshold and on the size of the clusters. In particular for sizes in the inertial range of scales and high thresholds, approximately layer-like structures of vortices are extracted and visualized. Agreement of results with previous observations and known features of turbulence supports the validity of the proposed method to characterize the geometry of intense vorticity and strain regions in high-Re turbulence.

DOI： 10.1088/1742-6596/708/1/012004

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

DOI： 10.11316/jpsgaiyo.71.1.0_3108

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Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：日本流体力学会  

High vorticity regions obtained by the large-scale direct numerical simulations with up to 122883 grid points, of forced incompressible turbulence in a periodic box are visualized using the method developed for handling such large-scale data. The visualization shows that in high Reynolds number turbulence, strong micro-scale vortices are dense in clusters of various sizes up to

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

Direct numerical simulations of turbulent boundary layers (TBL) along a flat plate are used to study the properties of turbulent/non-turbulent (T/NT) interface of the TBL. The values of the momentum-thickness-based Reynolds numbers, Re-theta, used for this study, are 500-2200. Analysis of the conditional statistics near the interface of the TBL shows that there are a small peak in the spanwise voracity, and an associated small jump in streamwise velocity. It is shown that the interfacial layer has an inertia-viscous double structure which consists of a turbulent sublayer with a thickness of the order of the Taylor micro-scale and its outer boundary with a thickness of the order of the Kolmogorov length scale. The velocity jump near the TINT interface of the TBL is of the order of the rms value of velocity fluctuations near the interface. Conditional cross correlations of the streamwise or the wall-normal velocity fluctuations change sharply across the interface, which are consistent with the blocking mechanism of the interface. 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license

DOI： 10.1016/j.jfluidstructs.2014.10.008

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

Statistics on the motion of small heavy (inertial) particles in turbulent flows with a high Reynolds number are physically fundamental to understanding realistic turbulent diffusion phenomena. An accurate parallel algorithm for tracking particles in large-scale direct numerical simulations (DNSs) of turbulence in a periodic box has been developed to extract accurate statistics on the motion of inertial particles. The tracking accuracy of the particle motion is known to primarily depend on the spatial resolution of the DNS for the turbulence and the accuracy of the interpolation scheme used to calculate the fluid velocity at the particle position. In this study, a DNS code based on the Fourier spectral method and two-dimensional domain decomposition method was developed and optimised for the K computer. An interpolation scheme based on cubic splines is implemented by solving tridiagonal matrix problems in parallel.

DOI： 10.1007/978-3-319-21909-7_51

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Publishing type：Research paper (international conference proceedings)  

Simulation, PIV data, and local models show characteristics and conditional statistics of turbulence either side and within interfacial layers [I] depending on the mean profile and the presence of resistive/porous walls. Key words; turbulence, interface structure, conditional statistics, numerical models

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：The Japan Society of Mechanical Engineers  

We examine the effects of temperature non-uniformity and turbulence on homogeneous charge compression ignition (HCCI) of a homogeneous n-heptane/air mixture, using three-dimensional direct numerical simulations of the mixture flows. We use a reduced chemical reaction model for the HCCI combustion. Time evolutions of the flows are obtained under the initial conditions having three different initial velocity fluctuations at 4.0 MPa and with temperature fluctuation around 781 K. Heat-release by the low-temperature oxidation, a key reaction in the ignition process, is analyzed along the trajectories of the temperature gradients, using dissipation-elements decomposition of the temperature fields. It is shown that the high heat-release rate occurs in the membrane-like regions where the temperature is about 870 K. The membrane-like regions move along the trajectories from high to low temperature. The analysis on the trajectories shows that the conditionally averaged moving speed and thickness of the regions are decreasing functions of the magnitude of temperature gradient. When the velocity fluctuation is strong, the turbulent flow is found to play a key role in retarding the ignition: The turbulent flow reduces the maximum temperature and slows down the averaged moving speed of the membrane-like regions.

DOI： 10.1299/transjsme.2014tep0

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

Three-dimensional tomographic time dependent PIV measurements of high Reynolds number (Re) laboratory turbulence are presented which show the existence of long-lived, highly sheared thin layer eddy structures with thickness of the order of the Taylor microscale and internal fluctuations. Highly sheared layer structures are also observed in direct numerical simulations of homogeneous turbulence at higher values of Re (Ishihara et al., Annu Rev Fluid Mech 41:165-180, 2009). But in the latter simulation, where the fluctuations are more intense, the layer thickness is greater. A rapid distortion model describes the structure and spectra for the velocity fluctuations outside and within 'significant' layers; their spectra are similar to the Kolmogorov (C R Acad Sci URSS 30:299-303, 1941) and Obukhov (Dokl Akad Nauk SSSR 32:22-24, 1941) statistical model (KO) for the whole flow. As larger-scale eddy motions are blocked by the shear layers, they distort smaller-scale eddies leading to local zones of down-scale and up-scale transfer of energy. Thence the energy spectrum for high wave number k is . The exponent p depends on the forms of the large eddies. The non-linear interactions between the distorted inhomogeneous eddies produce a steady local structure, which implies that 2p = 5/3 and a flux of energy into the thin-layers balancing the intense dissipation, which is much greater than the mean . Thence as in KO. Within the thin layers the inward flux energises extended vortices whose thickness and spacing are comparable with the viscous microscale. Although peak values of vorticity and velocity of these vortices greatly exceed those based on the KO scaling, the form of the viscous range spectrum is consistent with their model.

DOI： 10.1007/s10494-013-9518-0

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Using direct numerical simulation of turbulence in a periodic box driven by homogeneous forcing, with a maximum of 4096(3) grid points and Taylor micro-scale Reynolds numbers R (lambda) up to 1131, it is shown that there is a transition in the forms of the significant, high vorticity, intermittent structures, from isolated vortices when R (lambda) is less than 10(2) to complex thin-shear layers when R (lambda) exceeds about 10(3). Both the distance between the layers and their widths are comparable with the integral length scale. The thickness of each of the layers is of the order of the Taylor micro-scale lambda. Across the layers the velocity 'jumps' are of the order of the rms velocity u (o) of the whole flow. Within the significant layers, elongated vortical eddies are generated, with microscale thickness a"" (v) similar to 10 eta a parts per thousand(a)aEuro parts per thousand lambda, with associated peak values of vorticity as large as 35 omega (rms) and with velocity jumps as large as 3.4u (o) , where eta is the Kolmogorov micro scale and omega (rms) the rms vorticity. The dominant vortical eddies in the layers, which are approximately parallel to the vorticity averaged over the layers, are separated by distances of order a"" (v) . The close packing leads to high average energy dissipation inside the layer, as large as ten times the mean rate of energy dissipation over the whole flow. The interfaces of the layers act partly as a barrier to the fluctuations outside the layer. However, there is a net energy flux into the small scale eddies within the thin layers from the larger scale motions outside the layer.

DOI： 10.1007/s10494-013-9499-z

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

The role of turbulence in the combustion systems of flame propagation and diffusion combustion is to mix burned region with unburned region to promote combustion. Meanwhile homogeneous charged compression ignition (HCCI) is a combustion system which goes through the chemical reaction in overall field. It makes no rigid distinction between unburned region and burned region, and differs from the systems of flame propagation and diffusion combustion. Therefore, the role of turbulence in HCCI differs from other combustion systems. Three-dimensional direct numerical simulation (DNS) of auto-ignition process of n-heptane/air mixture was performed to analyze the interaction between chemical reaction and turbulence. In conclusions, the progress of chemical reaction delays under the area where rotation dominants in comparion with the area where distortion dominants under higher temperature region. Turbulence makes complicated structure of heat release which includes sheet and coherent structures. ©2013 The Japan Society of Mechanical Engineers.

DOI： 10.1299/kikaib.79.431

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Small-scale statistics in turbulent channel flow are studied by high resolution direct numerical simulations with the friction Reynolds number up to Re-tau = 2560. The second order velocity statistics in the inertial subrange of the log-low region are found to be not far from those predicted by Kolmogorov's universal equilibrium theory, although the agreement is not perfect. The shear parameter S* decreases with the distance y(+) from the wall and S* less than or similar to 0.1 in y(+) &gt; 400 for large Re-tau, where S* is the ratio of the Kolmogorov time scale to the mean shear time scale. For larger Re-tau, the y(+)-dependence of S* is closer to a simple theoretical estimate in the log-low region.

DOI： 10.1088/1742-6596/318/2/022016

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Data analysis of high resolution DNS of isotropic turbulence with the Taylor scale Reynolds number R-lambda = 1131 shows that there are thin shear layers consisting of a cluster of strong vortex tubes with typical diameter of order 10 eta, where eta is the Kolmogorov length scale. The widths of the layers are of the order of the Taylor micro length scale. According to the analysis of one of the layers, coarse grained vorticity in the layer are aligned approximately in the plane of the layer so that there is a net mean shear across the layer with a mean velocity jump of the order of the root-mean-square of the fluctuating velocity, and energy dissipation averaged over the layer is larger than ten times the average over the whole flow. The mean and the standard deviation of the energy transfer T(x, k) from scales larger than 1/k to scales smaller than 1/k at position x are largest within the layers (where the most intense vortices and dissipation occur), but are also large just outside the layers (where viscous stresses are weak), by comparison with the average values of T over the whole region. The DNS data are consistent with exterior fluctuation being damped/filtered at the interface of the layer and then selectively amplified within the layer.

DOI： 10.1088/1742-6596/318/4/042004

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Language：Japanese   Publishing type：Research paper (scientific journal)  

Two-dimensional direct numerical simulation (DNS) was applied to auto-ignition of n-heptane/air mixture. The diffusion of intermediate species was studied in terms of the influence on the ignition delay. The chemical reaction process. The simplified reaction mechanism was used in this study. Likewise, the influence of turbulence was investigated by comparing the results of 0 dimensional simulation and two-dimensional direct simulation of non-turbulence condition. In conclusions, the ignition delay was strongly affected by the different diffusion speeds of intermediate species. It was shown that the outflow of OH radical having larger diffusion coefficient decreases the reaction rate at the high temperature point. On the contrary, the reaction rate was enhanced by the influx of OH radical at the low temperature point. © 2011 The Japan Society of Mechanical Engineers. © 2012 The Japan Society of Mechanical Engineers.

DOI： 10.1299/kikaib.77.1592

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Language：English   Publisher：ANNUAL REVIEWS  

We review studies of the statistics of isotropic turbulence in an incompressible fluid at high Reynolds numbers using direct numerical simulation (DNS) from the viewpoint of fundamental physics. The Reynolds number achieved by the largest DNS, with 4096(3) grid points, is comparable with the largest Reynolds number in laboratory experiments. The high-quality DNS data in the inertial subrange and the dissipative range enable the examination of detailed statistics at small scales, such as the normalized energy-dissipation rate, energy and energy-flux spectra, the intermittency of the velocity gradients and increments, scaling exponents, and flow-field structure. We emphasize basic questions of turbulence, universality in the sense of Kolmogorov's theory, and the dependence of the statistics on the Reynolds number and scale.

DOI： 10.1146/annurev.fluid.010908.165203

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

Kolmogorov's 4/5 law is examined quantitatively by using the data of direct numerical simulations of incompressible turbulence in a periodic box with the number of grid points and the Taylor micro-scale Reynolds number 2048(3) and R-gimel approximate to 732, respectively. The examination is based on a generalization of the Karman-Howarth-Kolmogorov (KHK) equation for isotropic turbulence to anitropic turbulence. An emphasis is put on the influence of the finite Reynolds number, length-scale and the weak but finite anisotropy. The analysis of the DNS data gives a quantitative idea on the role of the viscous and forcing terms in the KHK equation. It also suggests that the anisotropy has substantial influence on the 4/5 law for a wide scale-range.

DOI： 10.1143/JPSJ.77.064401

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：CAMBRIDGE UNIV PRESS  

One-point statistics of velocity gradients and Eulerian and Lagrangian accelerations are studied by analysing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to 4096 3 grid points. The DNS consist of two series of runs; one is with k(max)eta similar to 1 (Series 1) and the other is with k(max)eta similar to 2 (Series 2), where k(max) is the maximum wavenumber and eta the Kolmogorov length scale. The maximum Taylor-microscale Reynolds number R-lambda in Series 1 is about 1130, and it is about 675 in Series 2. Particular attention is paid to the possible Reynolds number (Re) dependence of the statistics. The visualization of the intense vorticity regions shows that the turbulence field at high Re consists of clusters of small intense vorticity regions, and their structure is to be distinguished from those of small eddies. The possible dependence on Re of the probability distribution functions of velocity gradients is analysed through the dependence on R-lambda of the skewness and flatness factors (S and F). The DNS data suggest that the R-lambda dependence of S and F of the longitudinal velocity gradients fit well with a simple power law: S similar to -0.32R(lambda)(0.11) and F similar to 1.14(lambda)(0.34), in fairly good agreement with previous experimental data. They also suggest that all the fourth-order moments of velocity gradients scale with R-lambda similarly to each other at R-lambda &gt; 100, in contrast to R-lambda &lt; 100. Regarding the statistics of time derivatives, the sccond-order time derivatives of turbulent velocities are more intermittent than the first-order ones for both the Eulerian and Lagrangian velocities, and the Lagrangian time derivatives of turbulent velocities are more intermittent than the Eulerian time derivatives, as would be expected. The flatness factor of the Lagrangian acceleration is as large as 90 at R-lambda approximate to 430. The flatness factors of the Eulerian and Lagrangian accelerations increase with R-lambda approximately proportional to R-lambda(alpha E) and R-lambda(alpha L), respectively, where alpha(E) approximate to 0.5 and alpha(L) approximate to 1.0, while those of the second-order time derivatives of the Eulerian and Lagrangian velocities increases approximately proportional to R-lambda(beta E) and R-lambda(beta L), respectively, where beta(E) approximate to 1.5 and beta(L) approximate to 3.0.

DOI： 10.1017/S0022112007008531

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Language：Japanese   Publisher：The Japan Society for Industrial and Applied Mathematics  

DOI： 10.11540/bjsiam.15.3_280

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The static pressure fluctuation in a fully developed turbulence was measured. The aim was to determine how the spectral form varies depending on the Reynolds number. In particular, the spectral exponent and constant Kp were studied from the standpoint of Kolmogorov scaling. Probability density functions were computed and compared with DNS in order to ascertain the qualitative accuracy.

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DOI： 10.11316/jpsgaiyo.70.2.0_2807

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Language：Japanese   Publisher：一般社団法人情報処理学会  

現在日本最速のスーパーコンピュータである 「京」 を用いて,一様等方性乱流の超大規模直接数値シミュレーション (DNS) を実現するために,地球シミュレータ向けに開発された,フーリエ・スペクトル法に基づく一様等方性乱流の DNS コードの 「京」 への移植,及び最適化を行った.移植の際には,従来の 1 次元分割によるデータ分散手法から,より効率的な All-to-all 通信が可能であると考えられる 2 次元分割による手法へと変更を行った.その結果,「京」 の 192×128 ノードを用いて最大格子点数 122883 の超大規模 DNS の実現に成功した.これはプロダクトランとしては世界最大の一様等方性乱流の DNS である.ピーク性能比として,格子点数 61443,81923,122883 の DNS でそれぞれ 3.84%,3.14%,2.24% の実効性能が得られた.また,コードの更なる高効率化のために,乱流 DNS 特有のアルゴリズムに対する最適化を試み,その性能評価を行った.

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Language：Japanese   Publisher：一般社団法人情報処理学会  

現在日本最速のスーパーコンピュータである 「京」 を用いて,一様等方性乱流の超大規模直接数値シミュレーション (DNS) を実現するために,地球シミュレータ向けに開発された,フーリエ・スペクトル法に基づく一様等方性乱流の DNS コードの 「京」 への移植,及び最適化を行った.移植の際には,従来の 1 次元分割によるデータ分散手法から,より効率的な All-to-all 通信が可能であると考えられる 2 次元分割による手法へと変更を行った.その結果,「京」 の 192×128 ノードを用いて最大格子点数 122883 の超大規模 DNS の実現に成功した.これはプロダクトランとしては世界最大の一様等方性乱流の DNS である.ピーク性能比として,格子点数 61443,81923,122883 の DNS でそれぞれ 3.84%,3.14%,2.24% の実効性能が得られた.また,コードの更なる高効率化のために,乱流 DNS 特有のアルゴリズムに対する最適化を試み,その性能評価を行った.

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Language：Japanese   Publisher：京都大学  

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Other Link： http://hdl.handle.net/2433/223374

Language：Japanese   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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A review is given on studies of statistics at small scales in turbulent flows from a view point of universality. It is assumed in the view that the statistics at sufficiently small scales in the absence of mean flow are at a certain kind of local equilibrium state, and the influence of the mean flow may be regarded as a perturbation added to the equilibrium state. This idea has been examined by comparison of spectral characteristics derived by the idea with those in turbulent boundary layers, mixing layers and direct numerical simulations (DNS) of homogeneous turbulent shear flow. The applicability of this idea to turbulent channel flows is discussed in the light of the data of the log-law region in DNS of turbulent channel flows with the friction Reynolds number Ret up to 5120.

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Language：English   Publisher：Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology  

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Language：English   Publisher：IOP PUBLISHING LTD  

The probability density functions (PDFs) of energy dissipation rates created from the whole of the DNS region of the size 4096(3) (named whl-PDFs) for various sizes of coarse graining areas are analyzed by multifractal PDF theory (MPDFT). Furthermore, other PDFs named max-PDF and mm-PDF for various sizes of coarse graining areas, created respectively from the partial DNS regions of the size 512(3) with maximum and minimum enstrophy, are also analyzed by making use of the whl-PDF. It is shown that there is a whl-PDF with an appropriate size of coarse graining area, whose slope of the tail part can adjust the slope of the tail-part of a max-PDF. On the other hand, there is a whl-PDF whose center part can adjust quite accurately the center part of a min-PDF. Note that the partial DNS region with maximum (minimum) enstrophy is the region of maximally dense (rare) vortexes, and therefore contributes mainly to the tail (center) part of the whl-PDF. It is found that these adjustments are systematic with respect to the sizes of coarse graining areas.

DOI： 10.1088/1742-6596/410/1/012083

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Language：Japanese   Publishing type：Internal/External technical report, pre-print, etc.   Publisher：京都大学  

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Other Link： http://hdl.handle.net/2433/194442

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Language：English   Publisher：CELL PRESS  

The actomyosin interaction plays a key role in a number of cellular functions. Single-molecule measurement techniques have been developed to study the mechanism of the actomyosin contractile system. However, the behavior of isolated single molecules does not always reflect that of molecules in a complex system such as a muscle fiber. Here, we developed a simple method for studying the kinetic parameters of the actomyosin interaction using small numbers of molecules. This approach does not require the specialized equipment needed for single-molecule measurements, and permits us to observe behavior that is more similar to that of a complex system. Using an in vitro motility assay, we examined the duration of continuous sliding of actin filaments on a sparsely distributed heavy meromyosin-coated surface. To estimate the association rate constant of the actomyosin motile system, we compared the distribution of experimentally obtained duration times with a computationally simulated distribution. We found that the association rate constant depends on the sliding velocity of the actin filaments. This technique may be used to reveal new aspects of the kinetics of various motor proteins in complex systems.

DOI： 10.1016/j.bpj.2012.07.014

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Language：English   Publisher：The Japan Society of Mechanical Engineers  

A two-dimensional direct numerical simulation (DNS) was applied to investigate the autoignition process of an n-heptane/air mixture. The diffusion of intermediate species was studied in terms of the influence on the ignition delay period and the chemical reaction process. A simplified reaction mechanism was used in this study. The influence of turbulence was investigated by comparing the results of a zero-dimensional simulation and two-dimensional direct simulation of a non-turbulence condition. It was found that the ignition delay period was strongly affected by the different diffusion rates of intermediate species. It was shown that the outflow of OH radicals having a larger diffusion coefficient reduces the reaction rate at the high temperature point. In contrast, the reaction rate was enhanced by the influx of OH radicals at the low temperature point.

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Other Link： https://projects.repo.nii.ac.jp/?action=repository_uri&item_id=377158

Language：English  

A two-dimensional direct numerical simulation (DNS) was applied to investigate the autoignition process of an n-heptane/air mixture. The diffusion of intermediate species was studied in terms of the influence on the ignition delay period and the chemical reaction process. A simplified reaction mechanism was used in this study. The influence of turbulence was investigated by comparing the results of a zero-dimensional simulation and two-dimensional direct simulation of a non-turbulence condition. It was found that the ignition delay period was strongly affected by the different diffusion rates of intermediate species. It was shown that the outflow of OH radicals having a larger diffusion coefficient reduces the reaction rate at the high temperature point. In contrast, the reaction rate was enhanced by the influx of OH radicals at the low temperature point. Copyright © 2012 by the Japan Society of Mechanical Engineers.

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Language：Japanese   Publisher：一般社団法人日本物理学会  

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Other Link： https://projects.repo.nii.ac.jp/?action=repository_uri&item_id=376799

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Vortical structures and conditional statistics near the turbulent/non-turbulent interface of a turbulent mixing layer are studied using the data obtained by direct numerical simulation. We determine the conditional statistics by averaging data at fixed distances relative to the interface and put our emphasis on the possible Reynolds number (Re) dependence of the conditional statistics. Our analysis suggests that the conditionally-averaged spanwise vorticity has a sharp peak near the interface, and also that the width of the peak is approximately 10η irrespective of Re, where η is the Kolmogorov length scale.

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Language：Japanese   Publisher：The Japan Society of Mechanical Engineers  

Spectral direct numerical simulations (DNSs) of zero-pressure-gradient turbulent boundary layer along a flat plate are performed using a fringe method. In the DNSs a particular attention is paid to the possible effect of the fringe method on the statistics of turbulent boundary layer. Comparing the results obtained from DNSs of different parameters, we confirmed that there is a region for which similar Re-dependence of the statistics is obtained. DNS results show that Re-dependence of not only velocity statistics but also pressure statistics is quantitatively consistent with experimental results of much higher Re turbulent boundary layers.

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Language：Japanese   Publishing type：Internal/External technical report, pre-print, etc.  

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Language：English   Publishing type：Research paper, summary (national, other academic conference)   Publisher：SPRINGER-VERLAG BERLIN  

A review is given of the basic idea and some results of data-analysis of recent high-resolution direct numerical simulations (DNSs) of incompressible turbulence in a periodic box with up to 4096(3) grid points. Emphasis is put on the possible universality of small-scale statistics in turbulence at high Reynolds numbers. An analogy of turbulence with systems at or near thermal equilibrium state is also discussed.

DOI： 10.1007/978-3-642-00262-5_3

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We perform spectral direct numerical simulations (DNSs) of zero-pressure-gradient turbulent boundary layer along a flat plate using a fringe method. In the DNSs a particular attention is paid to the possible effect of the fringe method on the statistics of turbulent boundary layer. Comparing the results obtained from DNSs of different parameters, we confirmed that there is a region for which similar Re-dependence of the statistics is obtained. Visualizations of turbulent boundary layer show that |ω|, |∇p| and |∂p/∂x| have similar structures. This suggest a possibility that structures in high Re turbulent boundary layer may be understood by analyzing experimental data of ∂p/∂x.

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

Taylor microscale Reynolds numbers R_λ and one-dimensional energy spectra of the velocity fluctuations in turbulent channel flows are analyzed by using direct numerical simulations with friction Reynolds numbers up to Re_Τ=1280. Special emphasis is put on the dependence of R_λ on the distance from the wall and Re_Τ.

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Language：Japanese   Publisher：名古屋大学情報連携基盤センター  

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Multifractal analysis based on the energy dissipation epsilon and the enstrophy Omega in isotropic turbulence is made by using high-resolution direct numerical simulation of turbulence with the number of grid points up to 20483. The analysis shows that the singularity exponents alpha and alpha' that characterize the intermittencies associated with epsilon and Omega, respectively, agree well with each other in the inertial subrange. This result is consistent with log epsilon(r) and log Omega(r) correlating well with each other for the scale r in the inertial subrange, where the subscript denotes the local average over a cubic domain of size r.

DOI： 10.1007/978-1-4020-6472-2_9

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A review is presented on some attempts to understand turbulence by using high-performance computing (HPC). Among them is the study of turbulence by the direct numerical simulation (DNS) of incompressible turbulence in a periodic box with the number of grid points up to 4096(3). The DNS data shed some light on the Reynolds number (Re)-dependence of the statistics of turbulence at high Re and on the intermittency of energy dissipation. HPC is shown to be useful also for solving a multidimensional singular partial differential equation that determines the anomalous scaling of a passive scalar field advected by a random velocity field with an infinitely small correlation time.

DOI： 10.1007/978-1-4020-6472-2_7

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To study the properties of extreme events in Lagrangean acceleration we analyze Lagrangian data obtained from a direct numerical simulation of forced homogeneous isotropic turbulence which was performed on 1024^3 grid points with R 283. The extreme events are known to be trapping events by vortex filaments. Our analysis shows that the extreme Lagrangian accelerations are accompanied by spiral motions whose frequency is about 0.5Τ_η^1 and whose duration is less than about 10Τ_η, where Τ_η is the Kolmogorov time scale. It is found that the extreme events are strongly correlated with time variation of Lagrangian vorticities.

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)   Publisher：The Japan Society of Fluid Mechanics  

A review is presented on attempts to understand turbulence by using high-performance computing. An emphasis is puton the study of turbulence by the direct numerical simulation (DNS) of incompressible turbulence in a periodic boxwith the number of grid points up to 4096³. The DNS data shed some light on the basic questions on the statisticsof turbulence at high Reynolds number Re. The statistics include (i) the normalized mean rate of kinetic energydissipation in the limit Re→→, (ii) the energy spectrum in the universal equilibrium range, (iii) intermittency of thenergy dissipation rate, and (iv) energy transfer from large to small scales.

DOI： 10.11426/nagare1982.26.375

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Language：English   Publishing type：Research paper, summary (national, other academic conference)   Publisher：SPRINGER-VERLAG BERLIN  

We performed high-resolution direct numerical simulations (DNSs) of incompressible turbulence in a periodic box with the number of grid points up to 4096(3). The DNS data shed some light on the nature, especially on the possible universality, of small-scale statistics of turbulence at high Reynolds number Re. We report some results of the analysis of the DNS data with an emphasis on the possible dependence of the statistics on Re.

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

We performed high-resolution direct numerical simulations (DNS) of incompressible turbulence in a periodic box by using a Fourier spectral method with the number of grid points up to 4096(3). The simulations consist of two series: one with k(max)eta similar to 1 ( series 1), and the other with k(max)eta similar to 2 (series 2), where k(max) is the highest wavenumber in each simulation, and. is the Kolmogorov length scale. In the 4096(3) DNS, the Taylor scale Reynolds number R-lambda similar to 1200 and the ratio of L/eta of the integral length scale L to eta is approximately 2200, in series 1. The DNS data analysis reveals simple scaling of various spectra, and also sheds some light on (i) the energy spectrum at high R-lambda, (ii) the asymptotic R-lambda-dependence of the normalized energy dissipation rate, (iii) the anomalous scaling of the spectra of energy dissipation and enstrophy, and so on. After some preliminary remarks on the methods and limitations of the DNS, this paper presents a review of the DNS data analysis. Discussions are also made on some questions invoked by the DNS.

DOI： 10.1080/14685240500256099

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Pressure fluctuation is measured by using a condenser microphone and piezoresistive transducer. In order to confirm the experimental accuracy, measured data are compared with direct numerical simulation. This basic test encourages us to study small-scale statistics from the standpoint of Kohnogorov universal scaling. The power-law exponent and proportional constant of normalized pressure spectrum are discussed. The clear power law with scaling exponent -7/3 is confirmed in the range of R-lambda &gt;= 600. These Reynolds numbers are much larger than those in velocity fluctuation for achieving the Kolmogorov scaling. The spectral constant K-p is not universal but depends on Reynolds number.

DOI： 10.1007/1-4020-4181-0_17

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Multifractal analysis is performed by using the high-resolution DNS data of turbulence with the number of grid points up to 4096^3. The analysis shows that the so-called generalized dimensions of energy dissipation and enstrophy can be obtained as almost scale-independent expornents provided that the scale is in the inertial subrange. Reynolds number dependence of multifractal measures such as the so-called f(α) spectra is discussed.

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The statistics of energy transfer is studied by using the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence in a periodic box with the Taylor micro-scale Reynolds number R-lambda and grid points up to approximately 1130 and 4096(3), respectively. The data show that the energy transfer T across the wave number k is highly intermittent and the skewness S and flatness F of T increase with k approximately as S proportional to (kL)(alpha S), F proportional to (kL)(alpha F) in the inertial subrange, where alpha(S) similar to 2/3, alpha(F) similar to 1 and L the characteristic length scale of energy containing eddies. The comparison between the statistics of T, the energy dissipation rate epsilon and its average epsilon(r) over a domain of scale r shows that T is less intermittent than epsilon, while there is a certain similarity between the probability distribution functions of T and epsilon(r).

DOI： 10.1143/JPSJ.74.3202

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Other Link： http://hdl.handle.net/2433/47436

Language：Japanese   Publishing type：Internal/External technical report, pre-print, etc.   Publisher：豊田理化学研究所  

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The energy spectrum in the near dissipation range of turbulence is studied by analyzing the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence in a periodic box with the Taylor micro-scale Reynolds number R-lambda and resolution ranging up to about 675 and 4096(3), respectively. The spectra in the Reynolds number range fit well to the form C(k eta)(alpha) exp(-beta k eta) in the wavenumber range 0.5 less than or similar to k eta less than or similar to 1.5, where eta is the Kolmogorov dissipation length scale and C, alpha and beta are constants independent of k. The values of alpha and beta decrease monotonically with R-lambda, and they are consistent with the conjecture that they approach to constants as R-lambda -&gt; infinity, but the approach, especially that of beta, is slow.

DOI： 10.1143/JPSJ.74.1464

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Energy flux in turbulence from scales larger than a filter size γ to small scales is given by T(x, t)=-Τ_<ij>S^^-_<ij>, where Τ_<ij> is the subgrid stress and S^^-_<ij> is the resolved strain-rate tensor. The statistics of T is studied by using the data of a series of high-resolution direct numerical simulations of incompressible turbulence in a periodic box with the number of grid points up to 4096^3. The data show that T is highly intermittent and the skewness S and flatness F of T increase with the wavenumber κ(∝1/γ) approximately as S ∝(κL)^<αS> F ∝(κL)^<αF> in the inertial subrange, where α_S and α_F are constants independent of R_λ, and L is the characteristic length scale of energy containing eddies. The relation between the statistics of T, the energy dissipation rate ε and its local average ε_γ over a domain of scale r is also studied; T is less intermittent than ε and there is a certain similarity in the probability distribution functions of T and ε_γ.

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Language：English   Publisher：ELSEVIER SCIENCE BV  

The Earth Simulator (ES) is an SMP cluster system. There are two types of parallel programming models available on the ES. One is a flat programming model, in which a parallel program is implemented by MPI interfaces only, both within an SMP node and among nodes. The other is a hybrid programming model, in which a parallel program is written by using thread programming within an SMP node and MPI programming among nodes simultaneously. It is generally known that it is difficult to obtain the same high level of performance using the hybrid programming model as can be achieved with the flat programming model.
In this paper, we have evaluated scalability of the code for direct numerical simulation of the Navier-Stokes equations on the ES. The hybrid programming model achieves the sustained performance of 346.9Gflop/s, while the flat programming model achieves 296.4Gfiop/s with 16 PNs of the ES for a DNS problem size of 256 3. For small scale problems, however, the hybrid programming model is not as efficient because of microtasking overhead. It is shown that there is an advantage for the hybrid programming model on the ES for the larger size problems. (C) 2004 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.parco.2004.09.006

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

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Language：English   Publishing type：Research paper, summary (national, other academic conference)   Publisher：TSINGHUA UNIV PRESS  

We recently carried out a series of DNSs of incompressible turbulence with number of grid points up to 4096(3) on the Earth Simulator (ES). The 4096(3) (ultra) DNS is 64 times the size of the largest DNS before the appearance of the ES. The DNSs consist of two groups; one is with K-max eta = 2 R-lambda = 1 and the Taylor micro scale Reynolds number R-lambda = 167 similar to 1131, while the other is with K-max eta = 2 and R-lambda = 94 similar to 675, where K-max is the maximum wave number and eta the Kolmogorov length scale. A review is given on the one-point and two-point statistics of the velocity derivatives, including the fourth-order rotational invariants I-alpha (alpha = 1...4) proposed by Siggia (1981) and the spectra of energy dissipation epsilon, enstrophy omega(2), and pressure p, obtained by the series of the DNSs on the ES. The series of the DNSs suggest that the spectra of epsilon, omega(2), and p exhibited a wave number range in which the spectra scaled with the wave number k as k(-a). Exponent a for p was in good agreement with the value obtained by assuming the joint probability distribution of the velocity field to be Gaussian, while a values for epsilon and omega(2) were very different from the Gaussian approximation values.

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High-resolution direct numerical simulations (DNSs) of incompressible turbulence based on an alias-free spectral method were performed on the Earth Simulator. Statistics of turbulence are studied by a DNS on 1024(3) grid points with a special emphasis on the spectra of moments fourth order in velocity. A brief review is given on some results of the preliminary analysis of the data of DNSs with up to 2048(3) grid points.

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The data of high resolution direct numerical simulations (DNSs) of incompressible turbulence obeying the Navier-Stokes equations in a periodic box with the number of grid points up to 4096^3 were analyzed to study the one-point statistics of the velocity-derivatives, including probability distribution functions and the fourth-order rotational invariants I_α(α=1,2,3,4) proposed by Siggia (1981). The data suggest that the values of all four I_α(α=1,2,3,4) increase with the Reynolds number R_λ and the ratios I_α/I_l tend to constants with the increase of R_λ, and that they scale with R_λ similarly to each other for large R_λ.

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Language：English   Publisher：AMER PHYSICAL SOC  

Pressure fluctuation was measured in a turbulent jet using a condenser microphone and piezoresistive transducer. The power-law exponent and proportional constant of normalized pressure spectrum are discussed from the standpoint of Kolmogorov universal scaling. The clear power law with scaling exponent close to -7/3 was confirmed in the range of 600less than or equal toR(lambda). These Reynolds numbers are much larger than those in velocity fluctuation to achieve Kolmogorov scaling. The spectral constant is not universal but depends on Reynolds numbers. Measured pressure probability density functions are compared with direct numerical simulation.

DOI： 10.1103/PhysRevE.68.026309

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An analytical study of the anisotropic velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow is performed using a Lagrangian renormalized spectral closure approximation. The analysis shows that the spectrum in the asymptotic limit of infinitely large Reynolds numbers Re is determined by two nondimensional universal constants; theoretical estimates for the constants are provided. The anisotropic component of the spectrum at finite Re is more sensitive to large-scale turbulence structures than the isotropic component. A preliminary analysis of the effect of finite Re or the width of the inertial subrange is in qualitative agreement with direct numerical simulations. (C) 2003 American Institute of Physics.

DOI： 10.1063/1.1588307

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The spectra of the squares of velocity quadratics including the energy dissipation rate epsilon per unit mass, the enstrophy omega(2) and the pressure p were measured using the data obtained from direct numerical simulations (DNSs) of incompressible turbulence in a periodic box with number of grid points up to 2048(3). These simulations were performed using the Earth Simulator computing system. The spectra for epsilon, omega(2) and p exhibited a wave number range in which the spectra scaled with the wave number k as proportional to k(-a). Exponent a for p was about 1.81, which is in good agreement with the value obtained by assuming the joint probability distribution of the velocity field to be Gaussian, while a values for epsilon and omega(2) were about 2/3, and very different from the Gaussian approximation values.

DOI： 10.1143/JPSJ.72.983

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High-resolution direct numerical simulations (DNSs) of incompressible homogeneous turbulence in a periodic box with up to 4096(3) grid points were performed on the Earth Simulator computing system. DNS databases, including the present results, suggest that the normalized mean energy dissipation rate per unit mass tends to a constant, independent of the fluid kinematic viscosity nu as nu--&gt;0. The DNS results also suggest that the energy spectrum in the inertial subrange almost follows the Kolmogorov k(-5/3) scaling law, where k is the wavenumber, but the exponent is steeper than -5/3 by about 0.1. (C) 2003 American Institute of Physics.

DOI： 10.1063/1.1539855

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Language：English   Publisher：NEC CORP  

High-resolution direct numerical simulations (DNSs) of incompressible turbulence with numbers of grid points up to 2048(3) have been executed on the Earth Simulator (ES). The DNSs are based on the Fourier spectral method, so that the equation for mass conservation is accurately solved. In DNSs based on the spectral method, most of the computation time is consumed in calculating the three-dimensional (3D) Fast Fourier Transform (FFT). In this paper, we tuned the 3D-FFT algorithm for the Earth Simulator and have achieved DNS at 16ATFLOPS on 2048(3) grid points.

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Language：Japanese   Publisher：Japan Society of Mechanical Engineers  

A finite difference method (FDM) is easier and cheaper to use than a spectral method (SM) in flows with complicated geometry, but is inferior to a SM in both accuracy and resolution. In this paper, effects of both accuracy and resolution in a FDM on the quality of incompressible turbulent flow description were studied by comparing a SM with a FDM in direct numerical simulations (DNS) of the three-dimensional freely decaying homogeneous turbulence with 1283 and 2563 grids. We adopted the higher-order method of lines and Fourier spectral method as a FDM and a SM, respectively. The value of the kinematic viscosity was determined so that the minimum value of Kmaxη in time was about 2 in the SM with 2563 grids. Here, Kmax and η are the maximum resolved wavenumber and the Kolmogorov length scale, respectively. The statistical quantities, such as the total energy, the energy dissipation ratio, obtained by the higher-order method of lines were in good agreement with those by the SM. Furthermore, comparing their DNS fields, we found that the performance of the 4th-order method of lines with 2563 grids was comparable to that of the SM with 1283 grids in which the minimum value of Kmaxη in time was about 1.

DOI： 10.1299/kikaib.69.541

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A systematic way for formulating large-eddy simulation (LES) models based on the Lagrangian renormalized approximation is presented. A spectral LES to simulate the energy spectrum and a probabilistic LES to simulate both the energy spectrum and the error spectrum are formulated for 3-dimensional turbulence and 2-dimensional turbulence with the inverse energy cascading range. The derived models axe free from any ad hoc parameters. The models are verified using high resolution numerical simulations with 512(3) grid points for 3-dimension and 1024(3) for 2-dimension.

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In numerical simulation of turbulent flows, it is usually difficult to obtain exact initial conditions and it is well known that initial uncertainty in high wavenumbers spreads toward large scale through nonlinear dynamics. These imply the limitation of the numerical prediction. We present here a series of numerical experiments to study the effect of data assimilation on the predictability of isotopic 3D turbulence. In the experiment we have two parameters K-c and T to control the data assimilation, where K-c is the maximum of the assimilated wavenumber range and T is the time interval of the assimilation. It is found not only that we can suppress the growth of uncertainty by data assimilation but also that we can reduce it under appropriate conditions on K-c and T. It is also found that there exists a critical K-c* such that if K-c &lt; K-c*, the uncertainty grows for any T.

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Results of direct numerical simulation (DNS) of incompressible homogeneous and isotropic forced turbulence with grid points up to 1024 3 are presented with emphasis on the time dependence of the turbulence statistics. The Taylor micro scale Reynolds number at a quasi-stationary state is 283 in the DNS with 1024 3 grid points, and the energy spectrum exhibits an universal equilibrium range. The results suggest that for R-lambda &gt; 280 or so, the energy dissipation rate normalized by the integral length scale and root-mean-square velocity is almost independent of R-lambda and is 0.44 - 0.45.

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Turbulent diffusion of a pair of fluid particles in 3-dimensional homogeneous and isotropic turbulence was studied using a high-resolution direct numerical simulation (DNS) with 1024(3) grid points. The DNS showed that the mean square of the distance deltax between the two fluid particles grows with time t as &lt;\deltax\(2)&gt;similar toCepsilont(3) in the inertial subrange, which is in agreement with Richardson (1926) and Obukhov (1941), where Capproximate to0.7 and epsilon is the mean dissipation rate per unit mass. A simple Lagrangian closure approximation for &lt;\deltax\(2)&gt; is shown to be in good agreement with the DNS. (C) 2002 American Institute of Physics.

DOI： 10.1063/1.1508443

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There are two programming models on the shared-memory architecure. One, called the flat programming, is using MPI, and the other, called the hybrid programming, is using MPI and shared-memory models simultaneously. In general, it is difficult that the hybrid programming outperforms the flat programming. In this study, we evaluated a scalability of large-scale direct numerical simulations of the Navier-Stokes equations on the Earth Simulator. As a result, the hybrid programming could outpeform the flat programming on the Earth Simulator. Also, we discuss the tuning strategies to obtain higher performance on the Earth Simulator.

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Language：English   Publisher：AMER PHYSICAL SOC  

A simple theoretical analysis and direct numerical simulations on 512(3) grid points suggest that the velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow at high Reynolds number is given by a simple form that is an anisotropic function of the wave vector. The tensor is determined by the rate of the strain tensor of the mean flow, the rate of energy dissipation per unit mass, the wave vector, and two nondimensional constants.

DOI： 10.1103/PhysRevLett.88.154501

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The effects of wavenumber truncation on the direct numerical simulation (DNS) of incompressible turbulence at high Reynolds numbers using the Fourier spectral method were studied by comparing DNS fields with different truncation wavenumbers, K-max. The comparison suggests that the error due to truncation increases faster at higher wavenumbers, k, and the increase obeys a simple scaling law in the inertial subrange k much less than K-max. Some statistics, such as the energy and dissipation spectra, may remain insensitive to the error, even in the later period, provided that K(max)eta similar to 1 (eta is the Kolmogorov length scale), although DNS fields with different K-max are then essentially uncorrelated to each other.

DOI： 10.1143/JPSJ.71.777

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The high-resolution direct numerical simulations (DNSs) of incompressible turbulence with numbers of grid points up to 40963 have been executed on the Earth Simulator (ES). The DNSs are based on the Fourier spectral method, so that the equation for mass conservation is accurately solved. In DNS based on the spectral method, most of the computation time is consumed in calculating the three-dimensional (3D) Fast Fourier Transform (FFT), which requires huge-scale global data transfer and has been the major stumbling block that has prevented truly high-performance computing. By implementing new methods to efficiently perform the 3D-FFT on the ES, we have achieved DNS at 16.4 Tflops on 20483 grid points. The DNS yields an energy spectrum exhibiting a wide inertial subrange, in contrast to previous DNSs with lower resolutions, and therefore provides valuable data for the study of the universal features of turbulence at large Reynolds number.

DOI： 10.1109/SC.2002.10052

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It was shown by the authors [Phys. Rev. Lett. 88,154501 (2002)] that a perturbational analysis and direct numerical simulations on 512^3 grid points suggest a simple form of the velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow at high Reynolds number. It is an anisotropic function of the wavevector and determined by the rate of strain tensor of the mean flow, the energy dissipation per unit mass, and two non-dimensional constants. In this paper, and analysis to estimate the constants based on the Lagrangian renormalized approximation is presented. A preliminary analysis suggests that the anisotropic velocity correlation tensor at a wavenumber is sensitive to its ratio to the lower-end wavenumber of the inertial range.

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Nonlinear interactions between waves and turbulence cause systematic frequency shifts in Rossby waves. The frequency shifts in the inertial subranges of statistically steady beta -plane turbulence were examined theoretically and numerically. The theoretical analysis is based on the Lagrangian closure called the Lagrangian renormalized approximation and predicts that when the beta effect is small, the frequency shifts of Rossby waves are proportional to k(x)/k(4/3) in the inverse energy transfer range, while they are proportional to k(x) with or without a log-correction term in the enstrophy transfer range, depending on the flow conditions, where k(x) is the wave number in the eastward direction. Numerical simulations using 1024(2) grid points of forced beta -plane turbulence that exhibit the inertial subranges, show fairly good agreement with theoretical predictions. (C) 2001 American Institute of Physics.

DOI： 10.1063/1.1384468

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Other Link： http://hdl.handle.net/2433/41387

Language：English   Publisher：AMER INST PHYSICS  

A spectral closure analysis and numerical simulations suggest that there may be a class of two-dimensional turbulence in which the energy spectrum E(k) scales with the wave number k like E(k)=Ak(-3) in the enstrophy transfer range in accordance with the Kraichnan-Leith-Batchelor (KLB) spectrum, but the prefactor A is different from the KLB spectrum and depends in a nontrivial way on the flow conditions at large scales. (C) 2001 American Institute of Physics.

DOI： 10.1063/1.1359187

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Numerical simulations of two-dimensional forced turbulence suggest that the enstrophy transfer range energy spectrum E(k) a little steeper than k(-3) is robust in the sense that it may be realized in a wave number range under different run conditions. It is shown that such energy spectra fit well E(k)=C(K)eta (2/3)k(-3)[ln(k/k(1))](-1/3), where C-K is a dimensionless constant, eta the enstrophy transfer rate per unit mass and k(1) a wave number at the bottom of the range. The simulations give C(K)approximate to1.9 in fairly good agreement with the existing theoretical estimates. (C) 2001 American Institute of Physics.

DOI： 10.1063/1.1336149

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A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Padi approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales tau(L) and tau(E). An analysis of a high resolution (512(3) grid points) direct numerical simulation database at large Reynolds number suggests the scalings tau(L)proportional to k(-2/3) and tau(E) proportional to k(-1) for wave numbers k in the inertial subrange. The role of flow structures in turbulence in determining the time scales is also discussed. (C) 1999 American Institute of Physics. [S1070-6631(99)02508-8].

DOI： 10.1063/1.870077

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Language：English   Publisher：CAMBRIDGE UNIV PRESS  

A class of exact solutions of the Navier-Stokes equations is derived. Each of them represents the velocity field v = U + u of a thin vortical layer (a planar jet) under a uniform strain velocity field U in three-dimensional infinite space, and provides a simple how model in which nonlinear coupling between small eddies plays a key role in small-scale vortex dynamics. The small-scale structure of the velocity field is studied by numerically analysing the Fourier spectrum of u. It is shown that the Fourier spectrum of rr falls off exponentially with wavenumber k for large k. The Taylor expansion in powers of the coordinate (say y) in the direction perpendicular to the vortical layer suggests that the solution may be well approximated by a function with certain poles in the complex y-plane. The Fourier spectrum based on the singularities is in good agreement with that obtained numerically, where the exponential decay rate is given by the distance of the poles from the real axis of y.

DOI： 10.1017/S0022112098001293

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The time-derivatives up to the Gth-order of Eulerian and Lagrangian velocity fields in homogeneous and isotropic turbulence are computed. The Taylor expansions in powers of the time difference of the Eulerian as well as the Lagrangian two-time velocity correlations, and their Pade approximations are constructed from the time-derivatives. The Pade approximations are found to be in good agreement with direct numerical simulations.

DOI： 10.1143/JPSJ.67.1075

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The evolution of a small but finite three-dimensional disturbance on a flat uniform vortex sheet is analysed on the basis of a Lagrangian representation of the motion. The sheet at time t is expanded in a double periodic Fourier series: R(lambda(1),lambda(2),t) = (lambda(1),lambda(2),0) + Sigma(n,m) A(n,m) exp[i(n lambda(1) + delta m lambda(2))], where lambda(1) and lambda(2) are Lagrangian parameters in the streamwise and spanwise directions, respectively, and delta is the aspect ratio of the periodic domain of the disturbance. By generalizing Moore's analysis for two-dimensional motion to three dimensions, we derive evolution equations for the Fourier coefficients A(n,m). The behaviour of A(n,m) is investigated by both numerical integration of a set of truncated equations and a leading-order asymptotic analysis valid at large t. Both the numerical integration and the asymptotic analysis show that a singularity appears at a finite time t, = O(1n epsilon(-1)) where epsilon is the amplitude of the initial disturbance. The singularity is such that A(n,0) = O(t(c)(-1)) behaves like n-(5/2), while A(n)+/-1 = O(epsilon t(c),) behaves like n-(3/2) for large n. The evolution of A(0,m),(spanwise mode) is also studied by an asymptotic analysis valid at large t. The analysis shows that a singularity appears at a finite time t = O(epsilon(-1)) and the singularity is characterized by A(0,2k) proportional to k(5/2) for large k.

DOI： 10.1017/S0022112095003715

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Language：English   Publisher：PHYSICAL SOC JAPAN  

The three-dimensional motion of a flat uniform vortex sheet slightly perturbed initially in both streamwise and spanwise directions is studied on the basis of a Lagrangian representation of the motion. The vortex sheet at time t is represented as R(lambda1, lambda2, t) (lambda1, lambda2, 0) + SIGMA(n,m) A(n,m) (t) exp i(nlambda1 + mdeltalambda2), where lambda1 and lambda2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and delta is the aspect ratio of the periodic domain of the disturbance. The behaviour of A(n,0) and A(n,1) is studied by an asymptotic analysis valid at large t. The analysis shows that singularity appears on the sheet at a critical time 0 (In (epsilon1(-1))), where epsilon1 is the initial amplitude of the streamwise disturbance. The singularity is such that A(n,0) behaves like n-5/2 while A(n,1) behaves like n-3/2, for large n. The latter is associated with the vortex stretching intrinsic in three-dimensional dynamics of the sheet.

DOI： 10.1143/JPSJ.63.388

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Language：Japanese   Publishing type：Rapid communication, short report, research note, etc. (bulletin of university, research institution)   Publisher：Kyoto University  

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Language：Japanese   Publishing type：Internal/External technical report, pre-print, etc.  

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Language：English   Publisher：PHYSICAL SOC JAPAN  

Estimations of the time micro scales of Lagrangian strain tensors are obtained by dynamical analysis based on the Navier-Stokes equation for three dimensional turbulence at very high Reynolds number.

DOI： 10.1143/JPSJ.62.506

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Scopus

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Language：English   Publisher：PHYSICAL SOCIETY JAPAN  

A study is made of the stretching and distortion of material line elements in turbulence both analytically and numerically. Approximations for the statistics of these processes derived by perturbative expansions are tested by comparison with dynamical simulations in two dimensions. An integral time scale associated with the Lagrangian statistics of the velocity gradients plays a key role in the approximations. A rough estimation of the time scale is obtained by a dynamical short-time analysis by making use of the Navier-Stokes equation.

DOI： 10.1143/JPSJ.61.3547

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Language：Japanese   Publisher：統計数理研究所  

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Language：Japanese   Publisher：一般社団法人日本物理学会  

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Language：Japanese   Publishing type：Internal/External technical report, pre-print, etc.  

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Event date： 2023.10.23 - 2023.10.26

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Event date： 2022.9.27 - 2022.9.29

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Venue：京都大学 吉田キャンパス   Country：Japan  

Event date： 2022.9.27 - 2022.9.29

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Venue：京都大学 吉田キャンパス   Country：Japan  

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Venue：京都大学 吉田キャンパス   Country：Japan  

Event date： 2022.9.27 - 2022.9.29

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Venue：京都大学 吉田キャンパス   Country：Japan  

Event date： 2022.9.27 - 2022.9.29

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Event date： 2022.9.27 - 2022.9.29

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Event date： 2022.9.13 - 2022.9.15

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Venue：新潟大学（ハイブリッド）   Country：Japan  

Event date： 2022.9.13 - 2022.9.15

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Event date： 2022.5.28

Language：Japanese  

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Event date： 2022.5.22 - 2022.5.27

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Country：Japan  

Event date： 2022.5.22 - 2022.5.27

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Event date： 2022.3.9 - 2022.3.11

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Venue：Nagoya Institute of Technology (Online)   Country：Japan  

Event date： 2022.3.9 - 2022.3.11

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Event date： 2021.12.14 - 2021.12.16

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Event date： 2021.9.27 - 2021.9.28

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Event date： 2021.5.17 - 2021.5.19

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Event date： 2020.12.15 - 2023.12.17

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Venue：神戸大学先端融合研究環統合研究拠点 コンベンションホール  

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Venue：Lorentz Center@Oort  

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Venue：タワーホール船堀, 東京  

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Venue：東京工業大学  

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Venue：コクヨホール  

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Venue：名古屋工業大学  

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Venue：名古屋工業大学  

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Venue：愛媛大学  

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Venue：愛媛大学  

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Venue：THE GRAND HALL（品川）  

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Venue：筑波大学  

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Venue：沖縄青年会館（那覇市）  

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Venue：東京大学 物性研究所  

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Venue：九州大学 筑紫キャンパス  

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Venue：日本科学未来館  

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Venue：筑波大学  

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Venue：関西大学  

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Venue：関西大学  

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Venue：甲南大学  

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Venue：甲南大学  

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Venue：THE GRAND HALL（品川）  

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Venue：名古屋大学ES 総合館1 階ES ホール  

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Venue：国立天文台 三鷹キャンパス すばる棟大セミナー室  

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Venue：名古屋大学  

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Venue：タワーホール船堀, 東京  

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Venue：タワーホール船堀, 東京  

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Venue：小樽経済センター  

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Language：English   Presentation type：Oral presentation (general)