Distributions of Scalars in Basic Fluid Flows

Abstract:Mixing and transport of passive scalars is an important physical problem. Observed distributions of scalars in convection, the stratosphere and the ocean have heavy tails--large probabilities of large fluctuations. Mathematically, heavy tails have been found in random flows with and without chaos. We will investigate distributions of scalars in deterministic flows. We see heavy tails for shear flows, cellular flows and chaotic flows in certain parameter regimes and take a first step towards explaining the appearance of such distributions.