Universal and Non-Universal Features in the Random Shear Model

The stochastic transport of particles in a disordered two-dimensional layered medium,
driven by correlated y-dependent random velocity fields is usually referred to as random shear model.
This model exhibits a superdiffusive behavior in the x direction ascribable to the statistical properties
of the disorder advection field. By introducing layered random amplitude with a power-law discrete
spectrum, the analytical expressions for the space and time velocity correlation functions, together
with those of the position moments, are derived by means of two distinct averaging procedures. In
the case of quenched disorder, the average is performed over an ensemble of uniformly spaced initial
conditions: albeit the strong sample-to-sample fluctuations, and universality appears in the time
scaling of the even moments. Such universality is exhibited in the scaling of the moments averaged
over the disorder configurations. The non-universal scaling form of the no-disorder symmetric or
asymmetric advection fields is also derived.