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Research Article | Open Access

Sub-exponential mixing of generalized cellular flows with bounded palenstrophy

Gianluca Crippa( ), Christian Schulze
Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051 Basel, Switzerland
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Abstract

We study the mixing properties of a passive scalar advected by an incompressible flow. We consider a class of cellular flows (more general than the class in [Crippa-Schulze M 3AS 2017]) and show that, under the constraint that the palenstrophy is bounded uniformly in time, the mixing scale of the passive scalar cannot decay exponentially.

Keywords

mixingcontinuity equationflow of a vector fieldfluid dynamicspalenstrophy

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Mathematics in Engineering
Volume 5 Issue 1,
February 2023
Pages 1-12
DOI: 10.3934/mine.2023006

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Cite this article:
Crippa G, Schulze C. Sub-exponential mixing of generalized cellular flows with bounded palenstrophy. Mathematics in Engineering, 2023, 5(1): 1-12. https://doi.org/10.3934/mine.2023006

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Received: 12 August 2021
Revised: 20 December 2021
Accepted: 22 December 2021
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)