Work

Optimal mixing and enhanced dissipation for a smooth velocity field in any spatial dimension

Year: 2026

Type: preprint

Abstract: In this note, we consider the advection-diffusion equation on the $d$-dimensional torus, where $d$ is arbitrary. First, for the associated transport equation, we provide an explicit example of a space-time smooth, divergence-free, random velocity field that is a universal exponential mixer. Second, we set the molecular diffusivity to a (small) positive value, and we show that the same velocity field is dissipation enhancing with optimal rate. Our construction is based on the Random Dynamical Systems viewpoint, and relies on the uniform ergodicity of the two-point Markov process associated with the two-dimensional Pierrehumbert model.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.32535

Author: Melzi, Luca

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Imperial College London, Engineering and Physical Sciences Research Council

Award: EPSRC Centre for Doctoral Training in the Mathematics for our Future Climate: Theory, Data and Simulation

OpenAlex ID: W7214805634

Cites:

Cited by: 1

Related to: 10