3-DIMENSIONAL OSCILLATORY CONVECTION IN A GRAVITATIONALLY MODULATED FLUID LAYER

The equations for three-dimensional, time-dependent convection in a gr avitationally modulated fluid layer heated from below are solved numer ically using the Galerkin method in space and a Crank-Nicolson scheme in time. Nonlinear solutions are obtained for the Prandtl number of ai r (0.71) and for two Rayleigh numbers above the value for onset of osc illatory convection. Multiples of the fundamental frequency of oscilla tory convection were chosen in order to study the effects of possible resonances of the frequency of gravitational modulation. Modulation ca uses a transition from traveling wave convection, which persists in th e unmodulated case, to standing wave convection and phase locking occu rs for moderate values of the amplitude of the dimensionless gravitati onal modulation (scaled with the standard acceleration of gravity) in the range 0 to 3. For larger values of the modulation amplitude, frequ ency locking breaks down and chaotic time dependence occurs.