Energy spectrum of homogeneous and isotropic turbulence in far dissipation range

Abstract

The Kolmogorov relation for the third order structure function is used to derive the energy spectrum in the far dissipation range (k→∞). This contains no unspecified constants. Using methods from matched asymptotic expansions and mild analyticity assumptions, a uniformly valid form for the inertial through the dissipative ranges is obtained. An analogous energy spectrum is presented. This is compared with the results of physical and numerical experiments on the energy spectra E(k). The theoretical predictions are found to deviate by not more than a few percent from the measured data in the entire range of wave numbers where the energy spectrum E(k) varies by more than 30 orders of magnitude.