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)〉{~}t^2ν, with 2{ν}=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^δ) for u{}1, with {δ}=4/3. For an isotropic two-dimensional medium with uₓ(y)=f(y) and uy(x)=f(x), we find {ν}=2/3 and {δ}=1-{ν})^-1=3.