T. Clune and E. Knobloch
Pattern selection in rotating convection with experimental boundary conditions
Phys. Rev. E.
47 (1993) 2536-2550.
Small-amplitude Boussinesq convection in a plane layer with rigid, conducting boundaries rotating uniformly about a vertical axis is studied. A horizontally unbounded layer is modeled by periodic boundary conditions and the effect of mean-flow suppression by distant sidewalls is considered. An exact linear stability calculation partitions parameter space into regions of stationary and oscillatory convective onset. In the stationary regime, the critical Taylor number and critical angle for the onset of the Kuppers-Lortz instability are determined as a function of the Prandtl number sigma. Of the two competing two-dimensional patterns in the oscillatory regime, traveling waves are the preferred planform for 0.442 < sigma < 0.677. For sigma < 0.442 standing waves are preferred at onset for small rotation rates while traveling waves are preferred for larger rotation rates.