Patterns of Convection in Plane Layers and in Spherical Shells

Abstract

When a homogeneous fluid contained in a rectangular box is heated from below, the instability of the basic static state will be described in general by a single solution bifurcating from the primary solution of the problem. When the physical conditions are such that the two horizontal dimensions of the box are indistinguishable, the instability corresponds to a degenerate bifurcation problem, and the realized solution depends on the initial conditions of the experiment. This degeneracy can be called an orientational degeneracy, since it is associated with the two indistinguishable horizontal directions of the box.