### Abstract

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.

Original language | English |
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Pages (from-to) | 165-180 |

Number of pages | 16 |

Journal | Annual Review of Fluid Mechanics |

Volume | 41 |

DOIs | |

Publication status | Published - Jan 1 2009 |

Externally published | Yes |

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### Keywords

- Inertial subrange
- Intermittency
- Kolmogorov's theory
- Statistics
- Universality
- Visualization

### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Annual Review of Fluid Mechanics*,

*41*, 165-180. https://doi.org/10.1146/annurev.fluid.010908.165203

**Study of high-reynolds number isotropic turbulence by direct numerical simulation.** / Ishihara, Takashi; Gotoh, Toshiyuki; Kaneda, Yukio.

Research output: Contribution to journal › Review article

*Annual Review of Fluid Mechanics*, vol. 41, pp. 165-180. https://doi.org/10.1146/annurev.fluid.010908.165203

}

TY - JOUR

T1 - Study of high-reynolds number isotropic turbulence by direct numerical simulation

AU - Ishihara, Takashi

AU - Gotoh, Toshiyuki

AU - Kaneda, Yukio

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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 40963 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.

AB - 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 40963 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.

KW - Inertial subrange

KW - Intermittency

KW - Kolmogorov's theory

KW - Statistics

KW - Universality

KW - Visualization

UR - http://www.scopus.com/inward/record.url?scp=67649434198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649434198&partnerID=8YFLogxK

U2 - 10.1146/annurev.fluid.010908.165203

DO - 10.1146/annurev.fluid.010908.165203

M3 - Review article

VL - 41

SP - 165

EP - 180

JO - Annual Review of Fluid Mechanics

JF - Annual Review of Fluid Mechanics

SN - 0066-4189

ER -