Mixing and relaxation in ideal incompressible fluids

Abstract

In this paper we derive a necessary criterion for dissipation by mixing in ideal fluids. The experimental test of that criterion is simple and will help to discriminate real dissipation on microscopic scales from mixing relaxation in almost ideal fluids or 2-D magnetized electron plasmas. We will show how globally stable states do depend on the constraints resulting from incompressibility. And we will develop a model for the relaxation process on macroscopic scales bypassing the exact dynamics by using simple assumptions on filamentation of the density within the exact dynamics.