Magnetorotational instability suppression and Rayleigh-Bènard convection in a semi-infinite layer

Abstract

This work also demonstrates techniques for handling global phenomenon in the 3D Boussinesq equations on a semi-infinite domain; by considering the problem of rotating Rayleigh-Bènard convection; with non-periodicity in the y-axis, and with a semi-infinite geometry. For this problem, the absence of a periodic cell and the added boundary makes the techniques previously available for analyzing this flow unusable. Hence, a rigorous method is derived; and this uses a weighted generalized Lyapunov functional in a Sobolev embedded space, to show that rotation has a stabilizing effect on this flow. A weighted Toroidal-Poloidal decomposition is also considered as a more tractable approach for handling this type of problem.