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 esse ntially thermal inertial waves. The detailed structure of these modes is determined by balancing buoyancy forces against weak Viscous dissip ation and the objective here is to extend the results of Zhang and Rob erts into a finite amplitude regime. This paper presents the first stu dy of nonlinear thermo-inertial waves in a rapidly rotating layer usin g multiple timescales analysis and double expansion perturbations in t erms of small Ekman number and small amplitude. Some solutions of the nonlinear problem are given and the implications of our study for rela ted problems are considered.