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

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.