Symmetry and Symmetry-breaking Bifurcations in Fluid Dynamics

The recognition that fluid-dynamical models can yield solutions with less symmetry than the governing equations is not new. Jacobi's discovery that a rotating fluid mass could have equilibrium configurations lacking rotational symmetry is a famous nineteenth-century example. In modern terminology, Jacobi's asymmetric equilibria appear through a symmetry­ breaking bifurcation from a family of symmetric equilibria as the angular momentum (the "bifurcation parameter") increases above a critical value (the "bifurcation point"). Chandrasekhar (1969) gives a brief historical account of this discovery. In this example, as in many others, the presence of symmetry breaking was discovered by solving specific model equations. In contrast to this specificity, it is widely recognized that symmetry-breaking bifurcations are of frequent occurrence in a variety of nonlinear, nonequilibrium physical settings-fluids, chemical reactions, plasmas, and biological systems, to