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A crystallographic approach to symmetry-breaking in fluid layers

Accepted version
Peer-reviewed

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Authors

McKenzie, Dan 

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.

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Journal Title

Journal of Fluid Mechanics

Conference Name

Journal ISSN

0022-1120
1469-7645

Volume Title

Publisher

Cambridge University Press