Sub-exponential mixing of generalized cellular flows with bounded palenstrophy

TL;DR

This paper investigates how a passive scalar mixed by generalized cellular flows behaves under bounded palenstrophy, demonstrating that the mixing scale cannot decay exponentially over time.

Contribution

It extends previous work by analyzing a broader class of cellular flows and establishing sub-exponential mixing rates under palenstrophy constraints.

Findings

Mixing scale decay is sub-exponential for generalized cellular flows.

Bounded palenstrophy prevents exponential mixing rates.

Results apply to a more general class of flows than previously studied.

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 M3AS 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.