Novel late time asymptotics: applications to anomalous transport in turbulent flows

Abstract

New nonclassical self-similar intermediate asymptotics considered recently in the context of linear differential equations are shown to have interesting applications in offering a novel explanation of the origin of anomalous transport phenomena in turbulent flows in fluids and plasma devices. The intermediate asymptotics, in the late time or in the inviscid limit, conspire to produce smooth multifractal measures on a turbulent fluid medium leading naturally to generation of stretched Gaussian distributions for passive scalar tracer concentration from the turbulent, integral order, advection–diffusion equation. Such heavy-tailed stretched Gaussian distributions can explain the observed anomalous scaling of the average and mean square displacements of tracer particles in a turbulent medium.

Keywords:

• diffusion
• anomalous transport
• turbulent advection–diffusion equation

PACS:

• 47.21.-i;53.35.Ra