Bounds on the rate of enhanced dissipation

TL;DR

This paper establishes upper bounds on the exponential rates of enhanced dissipation in passive scalar mixing flows with diffusion, assuming certain integrability conditions on the velocity gradient, and confirms their optimality.

Contribution

It provides new upper bounds on enhanced dissipation rates under specific mathematical assumptions, advancing understanding of mixing efficiency.

Findings

Upper bounds on exponential dissipation rates are derived.

Results are shown to be optimal through recent constructions.

The work applies to flows with suitably integrable velocity gradients.

Abstract

We are concerned with flow enhanced mixing of passive scalars in the presence of diffusion. Under the assumption that the velocity gradient is suitably integrable, we provide upper bounds on the exponential rates of enhanced dissipation. Recent constructions indicate the optimality of our results.