Bifurcations in convection of incompressible fluid in a rotated square cylinder

Abstract

[Summary]: We consider two-dimensional convection of air in a long horizontal square cylinder two opposite side walls of which are thermally insulated and the other two are maintained at constant but different temperatures. The cylinder is gradually rotated about its horizontal axis so that the direction of the wall-to-wall temperature gradient changes with respect to the gravity vector: the cylinder is consecutively heated from the bottom, the side, the top and vice versa. It is found that a multitude of stationary bifurcating solution exist depending on the inclination angle and the Rayleigh number. Normally and abnormally rotating solutions are defined and distinguished and the bifurcation curve is computed for the first bifurcation resulting in an abnormally rotating convection roll.