Dissipation Enhancement by Mixing

TL;DR

This paper investigates how mixing processes enhance dissipation in fluid systems, providing quantitative estimates of dissipation time and energy decay based on mixing rates in both continuous and discrete models.

Contribution

It introduces a framework to quantify dissipation enhancement due to mixing, applicable to both continuous and discrete time dynamical systems, with explicit estimates based on mixing rates.

Findings

Dissipation time can be bounded using mixing rates.

Energy decay rates are quantitatively linked to mixing properties.

Mixing significantly accelerates dissipation in fluid systems.

Abstract

We quantitatively study the interaction between diffusion and mixing in both the continuous, and discrete time setting. In discrete time, we consider a mixing dynamical system interposed with diffusion. In continuous time, we consider the advection diffusion equation where the advecting vector field is assumed to be sufficiently mixing. The main results of this paper estimate the dissipation time and energy decay based on an assumption quantifying the mixing rate.