Reynolds number dependence of isotropic Navier-Stokes turbulence

Abstract

Reynolds number dependence of turbulence energy spectra and higher-order moments of velocity differences is explored by means of numerical integrations of the incompressible Navier-Stokes equation. The simulations have spatial resolutions up to ${512}^3$ and cover the range 15≤${\mathit{R}}_{\lambda }$≤200, where ${\mathit{R}}_{\lambda }$ is the Taylor microscale Reynolds number. Over this range, the energy spectra collapse when scaled by the wave number ${\mathit{k}}_{\mathit{p}}$ of peak dissipation and also by the spectrum level at ${\mathit{k}}_{\mathit{p}}$. It is found that ${\mathit{k}}_{\mathit{p}}$ varies with ${\mathit{R}}_{\lambda }$ in accord with the 1941 Kolmogorov theory. High-order normalized moments of velocity differences over inertial-range distances exhibit an ${\mathit{R}}_{\lambda }$-independent variation with separation distance. Implications of these observations are discussed.