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An exact derivation of the dissipation rate correlation exponent μin fully-developed turbulence

C. Jayaprakash·F. Hayot
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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.

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C. Jayaprakash, F. Hayot. 2002-01-17. An exact derivation of the dissipation rate correlation exponent μin fully-developed turbulence. https://arxiv.org/abs/nlin/0201033

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