Dislocation Dynamics in Rayleigh-B\'enard Convection

TL;DR

This paper investigates the dynamics of dislocations in Rayleigh-Bénard convection using theoretical models, revealing how forces from pattern changes and mean flows influence dislocation behavior and explain bound dislocation pairs.

Contribution

It introduces a comprehensive theoretical framework for dislocation motion in Rayleigh-Bénard convection, combining potential and non-potential forces, and explains experimental observations.

Findings

Dislocation motion is driven by Peach-Koehler and advection forces.

Bound dislocation pairs are explained by force competition.

Theoretical results align with experimental observations.

Abstract

Theoretical results on the dynamics of dislocations in Rayleigh-B\'enard convection are reported both for Swift-Hohenberg models and the Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven by the superposition of two independent contributions: (i) the Peach-Koehler force derived from the change of a Lyapunov potential with pattern wave number; (ii) a non-potential advection force on the dislocation core by its self-generated mean flow. Their competition allows for the first time to understand the experimentally observed bound dislocation pairs.