Dissipation enhancement of cellular flows in general advection diffusion equations

TL;DR

This paper extends the understanding of how cellular flows can enhance dissipation in various advection-diffusion equations, including hyper-diffusion and nonlinear diffusion, revealing flows that selectively enhance certain diffusive processes.

Contribution

It generalizes previous results on dissipation enhancement to more complex equations and identifies flows that enhance hyper-diffusion but not standard diffusion.

Findings

Existence of flows that enhance hyper-diffusion but not standard diffusion

Generalization of dissipation enhancement results to nonlinear diffusion equations

Identification of smooth incompressible flows with selective relaxation enhancement

Abstract

The main contribution of this paper is twofold: (1) Recently, Iyer, Xu, and Zlato\v{s} studied the dissipation enhancement by cellular flows based on standard advection-diffusion equations via a stochastic method. We generalize their results to advective hyper-diffusion equations and advective nonlinear diffusion equations. (2) We prove there exist smooth incompressible flows that are relaxation enhancing to hyper-diffusion but not to standard diffusion.