Anomalous fluctuations in tracer concentration in stratified media with random velocity fields

We find a quantitative law that describes the nature of the anomalous fluctuations in tracer concentration when diffusion occurs in a stratified medium, with drift velocities which are constant in the x direction, but vary randomly from layer to layer in the y direction. We find that the fluctuations of the tracer concentration P=P(x,t) are described by an extremely broad histogram of the form n(log10P)A/(log10P)3exp[-B/(log10P)2]. Moreover, the relative fluctuations P increase exponentially with x. Our results are supported by numerical calculations based on the method of exact enumeration.