The Existence of Anomalous Dissipation over Bounded Interior Domains

TL;DR

This paper demonstrates that anomalous energy dissipation, typically associated with turbulence, can occur even in linear Stokes flows within a bounded domain, challenging traditional views on turbulence mechanisms.

Contribution

It provides the first example of anomalous dissipation in a linear Stokes flow within a bounded domain, expanding understanding of dissipation phenomena beyond nonlinear turbulence.

Findings

Linear Stokes flow can exhibit anomalous dissipation.

Anomalous dissipation is not exclusive to nonlinear turbulence.

The example challenges existing assumptions about dissipation mechanisms.

Abstract

A prevalent feature of three-dimensional turbulence is the presence of anomalous dissipation, or that the mean rate of energy dissipation is bounded below by a positive number in the inviscid limit. This is thought to be due to the nonlinear convection term in the Navier Stokes equations stretching vortex tubules and thereby increasing the amount of small scale oscillations within the flow. In this paper, we construct an example of a linear Stokes flow within a sphere that exhibits anomalous dissipation.