TIME-PERIODIC THERMAL-CONVECTION IN HELE-SHAW SLOTS - THE DIAGONAL OSCILLATION

Numerical simulations show that the diagonal oscillation, previously observed in Benard convection experiments in Hele-Shaw slots, arises from an internal layer instability; an internal stagnation point is essential to the oscillation mechanism. This is contrasted with the more classical oscillation arising from a convected boundary-layer instability. From a dynamical systems viewpoint, the diagonal oscillation occurs in its purest form as a simultaneous temporal and spatial symmetry breaking (a Takens-Bogdanov bifurcation). Continuation methods yield the relevant bifurcation diagrams and show that the existence of the diagonal oscillation is robust with respect to modifications of the boundary conditions.