Finite amplitude thermal inertial waves in a rotating fluid layer

Recent investigations by Zhang and Roberts (1997) have shown that the onset of convection in a rapidly rotating fluid layer at sufficiently small Prandtl number and heated from below is via modes which are essentially thermal inertial waves. The detailed structure of these modes is determined by balancing buoyancy forces against weak viscous dissipation and the objective here is to extend the results of Zhang and Roberts into a finite amplitude regime. This paper presents the first study of nonlinear thermoinertial waves in a rapidly rotating layer using multiple timescales analysis and double expansion perturbations in terms of small Ekman number and small amplitude. Some solutions of the nonlinear problem are given and the implications of our study for related problems are considered.