Planform selection in rotating convection: Hexagonal symmetry

Three-dimensional convection in a rotating fluid layer is studied near the onset of a steady-state instability using equivariant bifurcation theory. The pattern selection problem is formulated as a bifurcation problem on a hexagonal lattice. Symmetry considerations determine the form of the ordinary-differential equations governing the evolution of the marginally stable modes. From the symmetry analysis the relative stability of the primary patterns can be determined. The theory is illustrated explicitly for idealized boundary conditions and the bifurcation diagrams given for all values of the Taylor and Prandtl numbers.