On asymptotics of a tracer advected in a locally self-similar,correlated flow

Abstract

In this paper we consider the motion of a tracer in a flow that is locally self-similar and whose correlations decay at infinity but at the rate that does not guarantee that the flow does not have “memory effect”. We show that when the field is Gaussian the appropriately regularized scaling limit of the trajectory is a super-diffusive fractional Brownian motion. This complements our previous result contained in Komorowski and Ryzhik (Nonlinearity, to appear).