Dissipation in Turbulent Solutions of 2-D Euler

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  • 30 October 2000
Abstract
We establish local balance equations for convex functions of the vorticity in the DiPerna-Majda weak solutions of 2D incompressible Euler, analogous to the balance proved by Duchon and Robert for kinetic energy in 3D. The anomalous term or defect distribution therein corresponds to the ``enstrophy cascade'' of 2D turbulence. It is used to define an appropriate notion of ``dissipative Euler solution'' in 2D. With any spatial H\"{o}lder regularity of the vorticity, even in a mean sense, the anomaly vanishes. We show that strong limits of 2D incompressible Navier-Stokes solutions for vanishing viscosity are dissipative weak solutions of Euler.

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