Sub-exponential mixing of generalized cellular flows with bounded palenstrophy

Gianluca Crippa; Christian Schulze; Gianluca Crippa; Christian Schulze

doi:10.3934/mine.2023006

Mathematics in Engineering

2023, Volume 5, Issue 1: 1-12. doi: 10.3934/mine.2023006

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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

Received: 12 August 2021 Revised: 20 December 2021 Accepted: 22 December 2021 Published: 17 January 2022

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$ ^3 $AS 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.
- mixing,
- continuity equation,
- flow of a vector field,
- fluid dynamics,
- palenstrophy
Citation: Gianluca Crippa, Christian Schulze. Sub-exponential mixing of generalized cellular flows with bounded palenstrophy[J]. Mathematics in Engineering, 2023, 5(1): 1-12. doi: 10.3934/mine.2023006

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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$ ^3 $AS 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.

References

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