Faculty Profiles - ISHIHARA Takashi

Papers - ISHIHARA Takashi

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Direct numerical simulations of compressible turbulence in a periodic box: Effect of isothermal assumptions on turbulence statistics Reviewed

Yoshiki Sakurai, Takashi Ishihara

Physics of Fluids 36 ( 8 ) 2024.8

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

Direct numerical simulations of compressible nonisothermal turbulence in a periodic box with up to 40963 grid points were conducted by varying Reynolds numbers and resolution levels. The results were compared with those of compressible isothermal turbulence by Sakurai and Ishihara [“Direct numerical simulations of compressible isothermal turbulence in a periodic box: Reynolds number and resolution-level dependence,” Phys. Rev. Fluids 8, 084606 (2023)] to study the effect of isothermal assumption on turbulence statistics. The turbulent Mach number and ratio of the dilatational to solenoidal root mean square velocities were fixed at approximately 0.3 and 0.4, respectively. A comparison under approximately equal flow conditions showed that the dilatational component of the energy spectra for the nonisothermal case exhibited approximately equal k−3 scaling at kη&gt;1 as observed for the isothermal case and was consistently smaller in the wavenumber range 0.05&lt;kη&lt;0.6 than that for the isothermal case, where η is the Kolmogorov length. The dilatational energy is mainly dissipated around kη≈0.3, the same wavenumbers as the solenoidal energy dissipation irrespective of the isothermal assumption. As the Reynolds number increased, the dilatational energy dissipation caused by shocklets around kη≈2 became larger, especially in the nonisothermal case. It was found that the isothermal assumption weakened the intermittency of the velocity divergence. No significant differences were observed in the normalized mean energy dissipation rates and pressure statistics. The local flow topology was also marginally affected by the isothermal assumption; however, the difference was significantly less than the changes owing to the different values of parameters such as the Reynolds number and Mach number.

DOI： 10.1063/5.0216518

File I/O Cache Performance of Supercomputer Fugaku Using an Out-of-Core Direct Numerical Simulation Code of Turbulence Reviewed

Yuto Hatanaka, Yuki Yamane, Kenta Yamaguchi, Takashi Soga, Akihiro Musa, Takashi Ishihara, Atsuya Uno, Kazuhiko Komatsu, Hiroaki Kobayashi, Mitsuo Yokokawa

Computational Science – ICCS 2024 173 - 187 2024.6

An Asymptotic Parallel Linear Solver and Its Application to Direct Numerical Simulation for Compressible Turbulence Reviewed

Mitsuo Yokokawa, Taiki Matsumoto, Ryo Takegami, Yukiya Sugiura, Naoki Watanabe, Yoshiki Sakurai, Takashi Ishihara, Kazuhiko Komatsu, Hiroaki Kobayashi

Computational Science – ICCS 2024 383 - 397 2024.6

Intermittency across Reynolds numbers – the influence of large-scale shear layers on the scaling of the enstrophy and dissipation in homogenous isotropic turbulence Reviewed

G.E. Elsinga, T. Ishihara, J.C.R. Hunt

Journal of Fluid Mechanics 974 2023.10

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

Direct numerical simulations up to Re_λ = 1445 show that the scaling exponents for the enstrophy and the dissipation rate extrema are different and depend on the Reynolds number. A similar Reynolds number dependence of the scaling exponents is observed for the moments of the dissipation rate, but not for the moments of the enstrophy. Significant changes in the exponents occur at approximately Re_λ ≈ 250, where Re_λ is the Taylor based Reynolds number, which coincides with structural changes in the flow, in particular the development of large-scale shear layers. A model for the probability density functions (PDFs) of the enstrophy and dissipate rate is presented, which is an extension of our existing model (Proc. R. Soc. A, vol. 476, 2020, p. 20200591) and is based on the mentioned development of large-scale layer regions within the flow. This model is able to capture the observed Reynolds number dependencies of the scaling exponents, in contrast to the existing theories which yield constant exponents. Moreover, the model reconciles the scaling at finite Reynolds number with the theoretical limit, where the enstrophy and dissipation rate scale identically at infinite Reynolds number. It suggests that the large-scale shear layers are vital for understanding the scaling of the extrema. Furthermore, to reach the theoretical limit, the scaling exponents must remain Reynolds number dependent beyond the present Re_λ range.

DOI： 10.1017/jfm.2023.799

Direct numerical simulations of compressible isothermal turbulence in a periodic box: Reynolds number and resolution-level dependence Reviewed

Yoshiki Sakurai, Takashi Ishihara

Physical Review Fluids 8 ( 8 ) 084606-1 - 084606-24 2023.8

I/O Performance Evaluation of a Memory-Saving DNS Code on SX-Aurora TSUBASA Reviewed

Mitsuo Yokokawa, Yuki Yamane, Kenta Yamaguchi, Takashi Soga, Taiki Matsumoto, Akihiro Musa, Kazuhiko Komatsu, Takashi Ishihara, Hiroaki Kobayashi

2023 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) 2023.5

Performance evaluation of parallel direct numerical simulation code on supercomputer SX-Aurora TSUBASA Reviewed

Mitsuo Yokokawa, Yujiro Takenaka, Takashi Ishihara, Kazuhiko Komatsu, Hiroaki Kobayashi

Computers and Fluids 261 105913 - 105913 2023.4

Non-local dispersion and the reassessment of Richardson's t3-scaling law Reviewed

G.E. Elsinga, T. Ishihara, J.C.R. Hunt

Journal of Fluid Mechanics 932 A17-1 - A17-32 2022.2

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

The Richardson-scaling law states that the mean square separation of a fluid particle pair grows according to <italic>t</italic>³ within the inertial range and at intermediate times. The theories predicting this scaling regime assume that the pair separation is within the inertial range and that the dispersion is local, which means that only eddies at the scale of the separation contribute. These assumptions ignore the structural organization of the turbulent flow into large-scale shear layers, where the intense small-scale motions are bounded by the large-scale energetic motions. Therefore, the large scales contribute to the velocity difference across the small-scale structures. It is shown that, indeed, the pair dispersion inside these layers is highly non-local and approaches Taylor dispersion in a way that is fundamentally different from the Richardson-scaling law. Also, the layer's contribution to the overall mean square separation remains significant as the Reynolds number increases. This calls into question the validity of the theoretical assumptions. Moreover, a literature survey reveals that, so far, <italic>t</italic>³ scaling is not observed for initial separations within the inertial range. We propose that the intermediate pair dispersion regime is a transition region that connects the initial Batchelor- with the final Taylor-dispersion regime. Such a simple interpretation is shown to be consistent with observations and is able to explain why <italic>t</italic>³ scaling is found only for one specific initial separation outside the inertial range. Moreover, the model incorporates the observed non-local contribution to the dispersion, because it requires only small-time-scale properties and large-scale properties.

DOI： 10.1017/jfm.2021.989

Statistics of local Reynolds number in box turbulence: ratio of inertial to viscous forces Reviewed

Yukio Kaneda, Takashi Ishihara, Koji Morishita, Mitsuo Yokokawa, Atsuya Uno

Journal of Fluid Mechanics 929 A1-1 - A1-19 2021.12

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

Effects of the Compressibility of Turbulence on the Dust Coagulation Process in Protoplanetary Disks Reviewed

Yoshiki Sakurai, Takashi Ishihara, Hitomi Furuya, Masayuki Umemura, Kenji Shiraishi

The Astrophysical Journal 911 ( 2 ) 140 - 140 2021.4

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

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

Thin Shear Layers in High-resolution Direct Numerical Simulations of Turbulence

Takashi Ishihara, Koji Morishita, J. C.R. Hunt

Notes on Numerical Fluid Mechanics and Multidisciplinary Design 147 517 - 526 2021

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

Optimizations of DNS Codes for Turbulence on SX-Aurora TSUBASA

Yujiro Takenaka, Mitsuo Yokokawa, Takashi Ishihara, Kazuhiko Komatsu, Hiroaki Kobayashi

Sustained Simulation Performance 2019 and 2020 51 - 59 2021

Drastic Changes of Turbulence in the Ignition Process of an n-Heptane/Air Mixture

Takashi Ishihara, Ryousuke Kuno

Lecture Notes in Mechanical Engineering 205 - 209 2021

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

Extreme dissipation and intermittency in turbulence at very high Reynolds numbers Reviewed

Gerrit E. Elsinga, Takashi Ishihara, Julian C. R. Hunt

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 ( 2243 ) 20200591 - 20200591 2020.11

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

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

Second-order velocity structure functions in direct numerical simulations of turbulence with Rλ up to 2250 Reviewed

Takashi Ishihara, Yukio Kaneda, Koji Morishita, Mitsuo Yokokawa, Atsuya Uno

Physical Review Fluids 5 ( 10 ) 104608-1 - 104608-15 2020.10

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

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

Thin shear layers in high Reynolds number turbulence - DNS results

T. Ishihara, J. C.R. Hunt, Y. Kaneda

ETC 2013 - 14th European Turbulence Conference 2020

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.

Thin shear layers in high Reynolds number turbulence - A coherent-structure model

J. C.R. Hunt, T. Ishihara, Y. Kaneda

ETC 2013 - 14th European Turbulence Conference 2020

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.

Dynamic geometrical analysis of high-enstrophy structures in isotropic turbulence

Yuji Hattori, Takashi Ishihara

ETC 2013 - 14th European Turbulence Conference 2020

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.

Estimation of turbulence-development by a multifractal theory

Toshihico Arimitsu, Naoko Arimitsu, Kohei Takechi, Yukio Kaneda, Takashi Ishihara

ETC 2013 - 14th European Turbulence Conference 2020

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.

Performance of a Two-Path Aliasing Free Calculation of a Spectral DNS Code Reviewed

Mitsuo Yokokawa, Koji Morishita, Takashi Ishihara, Atsuya Uno, Yukio Kaneda

ICCS 2019. Lecture Notes in Computer Science 11539 587 - 595 2019.6

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

Length Scales in Turbulent Channel Flow Reviewed

K Morishita, T Ishihara, Y Kaneda

Journal of the Physical Society of Japan 88 ( 6 ) 064401 2019.5

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

DISTRIBUTION AND MOTION OF INERTIAL PARTICLES AROUND HIGH VORTICITY REGIONS IN COARSE-GRAINED HOMOGENEOUS ISOTROPIC TURBULENCE

Yoshiki SAKURAI, Hiroki SHIRAISHI, Takashi ISHIHARA

Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) 75 ( 2 ) I_509 - I_518 2019

Relationships between Small-scale Fluid Motions and Inertial Particle Clustering in Turbulence Reviewed

Yoshiki Sakurai, Takashi Ishihara

Journal of the Physical Society of Japan 87 ( 9 ) 093401 - 0934014 2018.8

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

Dust Coagulation Regulated by Turbulent Clustering in Protoplanetary Disks Reviewed

Takashi Ishihara, Naoki Kobayashi, Kei Enohata, Masayuki Umemura, Kenji Shiraishi

ASTROPHYSICAL JOURNAL 854 ( 2 ) 81 2018.2

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

The scaling of straining motions in homogeneous isotropic turbulence Reviewed

GE Elsinga, T Ishihara, MV Goudar, CB da Silva, JCR Hunt

Journal of Fluid Mechanics 829 31 - 64 2017.9

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

Coherent structure extraction in turbulent channel flow using boundary adapted wavelets Reviewed

Teluo Sakurai, Katsunori Yoshimatsu, Kai Schneider, Marie Farge, Koji Morishita, Takashi Ishihara

JOURNAL OF TURBULENCE 18 ( 4 ) 352 - 372 2017

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

Energy spectrum in high-resolution direct numerical simulations of turbulence Reviewed

Takashi Ishihara, Koji Morishita, Mitsuo Yokokawa, Atsuya Uno, Yukio Kaneda

PHYSICAL REVIEW FLUIDS 1 ( 8 ) 082403 2016.12

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

Turbulence Near Interfaces-Modelling and Simulations Reviewed

J. C. R. Hunt, T. Ishihara, D. Szubert, I. Asproulias, Y. Hoarau, M. Braza

ADVANCES IN FLUID-STRUCTURE INTERACTION 133 ( 133 ) 283 - 292 2016

A new statistical tool to study the geometry of intense vorticity clusters in turbulence Reviewed

Alberto Vela-Martin, Takashi Ishihara

2ND MULTIFLOW SUMMER SCHOOL ON TURBULENCE 708 ( 708 ) 012004 2016

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

22aBU-9 Two-Point Statistics in Log-Law Region of Wall Bounded Turbulence : DNS-Data Analysis

Kaneda Y., Morishita K., Ishihara T.

Meeting Abstracts of the Physical Society of Japan 71 3108 - 3108 2016

高レイノルズ数乱流中の渦の組織構造とその時間発展

石原卓, 宇野篤也, 森下浩二, YOKOKAWA MITSUO, 金田行雄

第29回数値流体力学シンポジウム講演論文集 2015 1 - 5 2015.12

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

Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers Reviewed

Takashi Ishihara, Hiroki Ogasawara, Julian C. R. Hunt

JOURNAL OF FLUIDS AND STRUCTURES 53 50 - 57 2015.2

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

Accurate Parallel Algorithm for Tracking Inertial Particles in Large-Scale Direct Numerical Simulations of Turbulence

Takashi Ishihara, Kei Enohata, Koji Morishita, Mitsuo Yokokawa, Katsuya Ishii

PARALLEL COMPUTING TECHNOLOGIES (PACT 2015) 9251 522 - 527 2015

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

External and Internal interfacial turbulent shear layers

Julian Hunt, Takashi Ishihara, Jerke Eisma, Wim Paul Breugen, Jerry Westerweel, Marianna Braza

Proceedings - 15th European Turbulence Conference, ETC 2015 2015

A DNS study of the effects of temperature non-uniformity and turbulence on an auto-ignition process in a homogeneous n-heptane/air mixture Reviewed

ISHIHARA Takashi, ITO Takamasa, MIKI Takashi, YOSHIMATSU Katsunori, TERAJI Atsushi

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A 80 ( 820 ) 1-9 - TEP0361 2014.12

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

Thin Shear Layer Structures in High Reynolds Number Turbulence Tomographic Experiments and a Local Distortion Model

Julian C. R. Hunt, Takashi Ishihara, Nicholas A. Worth, Yukio Kaneda

FLOW TURBULENCE AND COMBUSTION 92 ( 3 ) 607 - 649 2014.3

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

Thin Shear Layers in High Reynolds Number Turbulence-DNS Results Reviewed

Takashi Ishihara, Yukio Kaneda, Julian C. R. Hunt

FLOW TURBULENCE AND COMBUSTION 91 ( 4 ) 895 - 929 2013.12

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

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

3D DNS analysis of interaction between turbulence and chemical reaction in an auto-ignition process under homogeneous n-heptane mixture Reviewed

Atsushi Teraji, Hironari Ikuta, Takashi Miki, Takashi Ishihara

Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B 79 ( 799 ) 431 - 438 2013

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

Small-scale statistics in direct numerical simulation of turbulent channel flow at high-Reynolds number Reviewed

Koji Morishita, Takashi Ishihara, Yukio Kaneda

13TH EUROPEAN TURBULENCE CONFERENCE (ETC13): WALL-BOUNDED FLOWS AND CONTROL OF TURBULENCE 318 ( SECTION 2 ) 022016 2011

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(+) > 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

Conditional analysis near strong shear layers in DNS of isotropic turbulence at high Reynolds number Reviewed

Takashi Ishihara, Julian C. R. Hunt, Yukio Kaneda

13TH EUROPEAN TURBULENCE CONFERENCE (ETC13): STATISTICAL ASPECTS, MODELLING AND SIMULATIONS OF TURBULENCE 318 ( SECTION 4 ) 042004 2011

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

Numerical analysis of intermediate species diffusion effect on low temperature oxidation in a homogeneous n-heptane mixture Reviewed

Atsushi Teraji, Masashi Nishida, Takahiro Morikawa, Takashi Ishihara, Yukio Kaneda

Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B 77 ( 779 ) 1592 - 1600 2011

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

Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation Reviewed

Takashi Ishihara, Toshiyuki Gotoh, Yukio Kaneda

ANNUAL REVIEW OF FLUID MECHANICS 41 165 - 180 2009

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

Examination of Kolmogorov's 4/5 law by high-resolution direct numerical simulation data of turbulence Reviewed

Yukio Kaneda, Junya Yoshino, Takashi Ishihara

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 77 ( 6 ) 064401 2008.6

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

Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics Reviewed

T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, A. Uno

JOURNAL OF FLUID MECHANICS 592 335 - 366 2007.12

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 > 100, in contrast to R-lambda < 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

Introduction to Spectral Methods

Ishihara Takashi

Bulletin of the Japan Society for Industrial and Applied Mathematics 15 ( 3 ) 280 - 281 2005

Similarity scaling of pressure fluctuation in turbulence

Yoshiyuki Tsuji, Takashi Ishihara

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 68 ( 2 2 ) 2003.8

Publishing type：Research paper (scientific journal)

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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