Time-periodic thermal convection in Hele–Shaw slots: The diagonal oscillation

Numerical simulations show that the diagonal oscillation, previously observed in Bénard 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.