Remarks on anomalous dissipation for passive scalars

A. L. Mazzucato

doi:10.1098/rsta.2021.0099

Remarks on anomalous dissipation for passive scalars

A. L. Mazzucato

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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)’.

Original language	English (US)
Article number	20210099
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	380
Issue number	2218
DOIs	https://doi.org/10.1098/rsta.2021.0099
State	Published - Mar 7 2022

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rsta.2021.0099

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AB - 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)’.

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Remarks on anomalous dissipation for passive scalars

Abstract

All Science Journal Classification (ASJC) codes

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