An oscillatory secondary bifurcation for magnetoconvection and rotating convection at small aspect ratio

We consider the dynamics of convection in a strong vertical magnetic field, and in the presence of rapid rotation. In both these cases, in circumstances which can be realized in the laboratory, the onset of convection is in the form of tall thin cells. Because of this, the dynamics near onset is characterized by an interaction between the cellular modes and the horizontally averaged temperature profile. The effects on the dynamics are slight in the case of a Boussinesq fluid. However in both cases, when the layer is stratified (non-Boussinesq), the convection can lose stability to oscillations close to onset. Properties of the oscillations and their stability to long-wavelength modulation are extensively investigated.