Relations between intermittency and structure function exponents in turbulence

We derive from the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function, <∈(x+r,t+τ)∈(x,t)>, which we study in the equal time limit, for homogeneous, isotropic turbulence. We exploit its mathematical similarity to the corresponding equation derived from the one-dimensional stochastic Burgers equation to show that the main intermittency exponents are μ₁ = 2 -ζ6 and μ₂ = 2Z̃⁴-ζ₄, where the ζ' S are exponents of velocity structure functions and Z̃₄ is a dynamical exponent characterizing the fourth order structure function. We discuss the role of sweeping and Galilean invariance in determining the intermittency exponents.