SUPERDIFFUSION IN RANDOM VELOCITY-FIELDS

We discuss the superdiffusive motion of a random walk in a medium containing random velocity fields. For a two-dimensional layered medium with y-dependent random velocities in the x direction u(y), x2(t)t2, with 2=3/2, and with strong sample-to-sample fluctuations. The probability distribution of displacements, averaged over environments, takes a non-Gaussian scaling form at large time, P(x,t)t-3/4f(x/t3/4), where v(u)exp(-u) for u1, with =4/3. For an isotropic two-dimensional medium with ux(y)=f(y) and uy(x)=f(x), we find =2/3 and =1-)-1=3. © 1990 The American Physical Society.