STRONGLY NONLINEAR CONVECTION CELLS IN A RAPIDLY ROTATING FLUID LAYER

We investigate the properties of some strongly nonlinear convection ce lls which map occur in a rapidly rotating fluid layer. Although the st ability properties of such layers have been extensively studied, most of the theoretical work concerned with this topic has been based upon either linear or weakly nonlinear analyses. However, it is well known that weakly nonlinear theory has a limited domain of validity for if t he amplitude of the convection cells becomes too large then the mean t emperature profile within the layer is dramatically perturbed away fro m its undisturbed state and the assumptions underpinning weakly nonlin ear theory break down. It is the case for most fluid stability problem s that when the stage is reached that the mean flow is significantly a ltered by the presence of instability modes, then analytical progress becomes impossible. The problem can then only be resolved by a numeric al solution of the full governing equations but we show that for the c ase of convection rolls within a rapidly rotating layer this sequence of events does not arise. Instead, the properties of large amplitude c onvection rolls (which are sufficiently strong so as to completely res tructure the mean temperature profile) can be determined by analytical methods. In particular, the whole flow structure can be deduced once a single, very simple eigenproblem has been solved. This solution enab les us to discuss how large amplitude cells can significantly affect t he characteristics of the flow leading to greatly enhanced heal transf er across the layer.