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

A crystallographic approach to symmetry-breaking in fluid layers