Bifurcation of infinite Prandtl number rotating convection

Abstract

We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park (2005, 2007, revised for publication) [5,6,25] under various boundary conditions. By thoroughly investigating we prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor Σ R which consists of only one cycle of steady state solutions and is homeomorphic to S 1 . We also see how intensively the rotation inhibits the onset of convective motion. This bifurcation analysis is based on a new notion of bifurcation, called attractor bifurcation which was developed by Ma and Wang (2005); see [15].