An equation for the dissipation rate correlation and its implications for the intermittency exponent μ in turbulence

We derive an equation satisfied by the dissipation rate correlation function, [epsilon ((x) over right arrow + (r) over right arrow, t + tau) epsilon((x) over right arrow, t)] for the homogeneous, isotropic state of fully-developed turbulence from the the Navier- Stokes equation. In the equal time limit we show that the equation leads directly to two intermittency exponents mu(1) = 2-zeta(6) and mu(2) = z(4)" -zeta(4), where the zeta' s are exponents of velocity structure functions and z(4)" is a dynamical exponent characterizing the fourth order structure function. We discuss the contributions of the pressure terms to the equation and the consequences of hyperscaling.