Remarks on anomalous dissipation for passive scalars

Abstract

We consider the problem of anomalous dissipation for passive scalars advected by an incompressible flow. We review known results on anomalous dissipation from the point of view of the analysis of partial differential equations, and present simple rigorous examples of scalars that admit a Batchelor-type energy spectrum and exhibit anomalous dissipation in the limit of zero scalar diffusivity. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.