Diffusion Approximation to Inertial Energy Transfer in Isotropic Turbulence

Abstract

A diffusion approximation is described to the nonlocal inertial energy transfer between wavenumber components in the spectral representation of an isotropic turbulent flow. The approximation yields Kolmogorov's inertial‐range spectrum and is shown to be the local limit of a class of approximations suggested by Kraichnan and Spiegel. A spectrum in the viscous dissipation range is computed with the diffusion approximation and compared to spectra obtained from approximations of Heisenberg and Kovasznay as well as a modification of Obukhov's approximation and a recent prediction of Kraichnan. It agrees closely with the last two. Similarity spectra and associated longitudinal correlation functions are computed for decaying turbulence at infinite Reynolds number. A comparison is made with corresponding results based on the Heisenberg approximation.