Pattern selection for the oscillatory onset in thermosolutal convection

A layer of fluid lies between two parallel horizontal walls and the solute concentration and temperature are higher at the bottom wall. The onset of time-periodic instability in this double diffusion problem in three dimensions is analyzed. Periodicity with respect to the hexagonal lattice is assumed. The no-slip condition is imposed at the top and bottom boundaries. There are 11 bifurcating solutions, and their stability is presented. For relatively low solutal and thermal Rayleigh numbers, the solutions are found to be unstable. For the heating of salty water, situations are presented where the standing rolls, the standing patchwork quilt, and either the standing hexagons or the standing regular triangles, may be stable.