A Governing Equation for the Small-Scale Turbulence

Abstract

The equation governing the motion of small eddies in turbulent flows is considered in connection with the physical background of Kolmogorov’s −5⁄3 power law. The nonlinear interaction in the Navier-Stokes equations is decomposed into the interaction of convection type between small and big eddies and that of distortion type among small eddies themselves. It is shown that an equation based on the distortion-type interaction only can be obtained by the use of a Galilean transformation. This equation is free from the difficulty of the divergence of the response equation at low wave numbers which is a stumbling block to the analytical derivation of Kolmogorov’s law.