Three Dimensional Modeling of Rayleigh-Benard Stabilization by Forced Domain Oscillation in a Thermally Unstably Stratified System

Recent experiments by our team and others have shown that the onset of Rayleigh-Bernard (R-B) instability can be delayed by suitable forced oscillation of unstably stratified flow systems. Our recent work includes experimental results obtained in a 4cm x 4cm x 1.5 cm high rectangular air chamber heated from the bottom, and subject to a host of oscillatory vertical motions. We have previously shown that Floquet stability theory predicts the location of the stability boundary in the Amplitude-Frequency plane, at least at the lower frequencies where data was obtained. In this work we solve the discrete weakly compressible (Boussinesq) time dependent Navier-Stokes (N-S) equations in a frame of reference affixed to the test fixture. We are able to predict 2D and 3D stability bounds in very close correspondence to the experimental data and stability theory. We also predict a rich complexity of R-B cell topologies in the low-aspect ratio, square cross section domain.