Thermosolutal Convection at Infinite Prandtl Number with or without Rotation: Bifurcation and Stability in Physical Space

We examine the nature of the thermosolutal convection with or without rotation in the infinite Prandtl number regime, which is applicable to magma chambers. The onset of bifurcation and the structure of the bifurcated solutions in this double diffusion problem are analyzed. The stress-free boundary condition is imposed at the top and bottom plates confining the fluid. For the rotation free case, 2-dimensional Boussinesq equations are considered and we prove that there are bifurcating solutions from the basic solution and that the bifurcated solutions consist of only one cycle of steady state solutions that are homeomorphic to S1. By thoroughly investigating the structure and transitions of the solutions of the thermosolutal convection problem in physical space, we confirm that the bifurcated solutions are indeed structurally stable. In the presence of rotation, we consider 3-dimensional Boussinesq equations and we can get similar results as of the rotation free case. We also see how intensively the rotation inhibits the onset of convective motion. In turn, this will corroborate and justify the suggested results with the physical findings about the presence of roll structure.