Chaotic advection in a steady three-dimensional MHD flow

TL;DR

This paper studies how steady 3D magnetohydrodynamic flows in a cubic cavity can produce chaotic advection, leading to efficient mixing, by analyzing flow structures, chaos indicators, and mixing metrics.

Contribution

It demonstrates that superimposing multiple recirculation cells in a steady MHD flow can induce chaos and enhance mixing, providing insights into flow control for mixing processes.

Findings

Chaotic advection is achieved through superposition of flow cells.

Flow analysis shows the presence of chaotic streamlines.

Mixing efficiency is significantly improved despite individual vortex limitations.

Abstract

We investigate the 3D stationary flow of a weakly conducting fluid in a cubic cavity, driven by the Lorentz force created by two permanent magnets and a weak constant current. Our goal is to determine the conditions leading to efficient mixing within the cavity. The flow is composed of a large recirculation cell created by one side magnet, superposed to two recirculation cells created by a central magnet perpendicular to the first one. The overall structure of this flow, obtained here by solving the Stokes equations with Lorentz forcing, is similar to the tri-cellular model flow studied by Toussaint et. al. (Phys. Fluids. 7, 1995). Chaotic advection in this flow is analyzed by means of Poincar\'e sections, Lyapunov exponents and expansion entropies. In addition, we quantify the quality of mixing by computing contamination rates, homogeneity, as well as mixing times. Though individual vortices have poor mixing properties, the superposition of both flows creates chaotic streamlines and efficient mixing.