An exact derivation of the dissipation rate correlation exponent \mu in fully-developed turbulence

Abstract

We derive for the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function. In the equal time limit, in the inertial range, for the homogeneous, isotropic state of fully-developed turbulence, we show that the correlation is characterized by two exponents, one of which depends on the sixth-order static structure function exponent and the other involves the behavior of the fourth-order dynamical structure function. This provides a direct derivation of the intermittency exponent of the dissipation-rate correlation.