Calculation of the diffusion coefficient in acoustic turbulence

The first (Born) approximation commonly used to calculate the diffusion coefficient D-T of a passive scalar in acoustic turbulence is shown to be insufficient. Even for a small main parameter-the Mach number, M < 1-the next approximation gives a larger contribution to D-T than does the first approximation, but negative in sign. We present a procedure for correctly calculating D-T based on the solution of a nonlinear DIA (direct interaction approximation) equation for the mean Green's function of the problem. We include an additional term in the general formula for D-T that directly describes the compressibility of acoustic turbulence. This term has not been known previously and has been disregarded even in the Born approximation. A positive value was obtained for D-T = CM(3)u(0)/p(0). The spectrum E(x) was assumed to be smooth at distances Deltax similar to M-2 < 1. (C) 2002 MAIK "Nauka / Interperiodica".