Planform selection in rotating convection

Three-dimensional convection in a rotating fluid layer is studied near the onset of the steady-state instability using symmetric bifurcation theory. The problem is formulated as a bifurcation problem on a doubly periodic square 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 rolls and squares can be determined. Stable solutions exist only if both patterns bifurcate supercritically, and the one with the largest Nusselt number is the stable one. The theory is illustrated by explicit calculations for idealized boundary conditions, and the bifurcation diagrams given for all values of the Taylor and Prandtl numbers