Leonid Piterbarg
University of Southern California, Department of Mathematics
(Abstract received 03/14/2012 for session D)
ABSTRACT
We present and analyze explicit FSLE expressions for several idealized models of turbulence in 1D and 2D. Among them are a random walk with discrete time and continuously distributed jumps and an isotropic Brownian flow in 2D also known as the Kraichnan flow. For the former a surprising fact is a '-1' scaling for small separations in contrast to '-2' well known for a random walk in continuous time (Brownian flow) and for a simple random walk in discrete time. For the Kraichnan flow an exact relation is established between the scaling of FSLE and the scaling of relative dispersion in time.