A crystallographic approach to symmetry-breaking in fluid layers

TL;DR

This paper introduces a crystallographic approach to analyze symmetry-breaking in fluid layers, leveraging group theory and crystallography databases to better understand fluid bifurcations, exemplified through thermal convection.

Contribution

It applies crystallographic layer groups to fluid dynamics, providing a novel, systematic way to describe and analyze symmetry-breaking bifurcations in fluid flows.

Findings

Crystallographic notation effectively describes fluid flow symmetries.

Crystallography databases can be used to analyze fluid bifurcations.

The approach simplifies understanding of symmetry transitions in fluid systems.

Abstract

Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from symmetry alone, using the theory of groups and their representations. Here we show how the extensive databases on groups in crystallography can be exploited to yield insights into fluid-dynamical problems. In particular, we demonstrate the application of the crystallographic layer groups to problems in fluid layers, using thermal convection as an example. Crystallographic notation provides a concise and unambiguous description of the symmetries involved, and we advocate its broader use by the fluid dynamics community.