ANOMALOUS SCALING OF A RANDOMLY ADVECTED PASSIVE SCALAR

Solenoidal advection in d dimensions may induce inertial-range behavior [\T(x, t) - T(x + r, t)\(n)] proportional to r(zeta n(T)) of a passive scalar field T(x, t). If the velocity field changes very rapidly in time, the zeta(n)(T) are determined by the two-particle eddy-diffusion coefficient eta(r) proportional to r(zeta(eta)). An approximation to the molecular-diffusion terms yields zeta(n)(T) = 1/2 root 2nd[2-zeta(eta)] + alpha(2) - 1/2 alpha where alpha = d + zeta(eta) - 2. As n --> infinity, zeta n(T) proportional to root nd.