Strongly nonlinear convection cells in a rapidly rotating fluid layer

We investigate the properties of some strongly nonlinear convection cells which may occur in a rapidly rotating fluid layer. Although the stability 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 the amplitude of the convection cells becomes too large then the mean temperature profile within the layer is dramatically perturbed away from its undisturbed state and the assumptions underpinning weakly nonlinear theory break down. It is the case for most fluid stability problems that when the stage is reached that the mean flow is significantly altered by the presence of instability modes, then analytical progress becomes impossible. The problem can then only be resolved by a numerical solution of the full governing equations but we show that for the case of convection rolls within a rapidly rotating layer this sequence of events does not arise. Instead, the properties of large amplitude convection rolls (which are sufficiently strong so as to completely restructure 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 enables us to discuss how large amplitude cells can significantly affect the characteristics of the flow leading to greatly enhanced heat transfer across the layer.