Fully nonlinear oscillatory convection in a rotating layer

Two-dimensional overstable convection in a rotating layer is studied for large Taylor numbers. In this regime, the leading order nonlinearity arises from the distortion of the horizontally averaged temperature profile. Fully nonlinear solutions in the form of traveling and standing waves are obtained via an asymptotic expansion in the Taylor number. The formulation leads to a nonlinear eigenvalue problem for the vertical structure and frequency of each solution type and allows the computation of the Nusselt number and frequency as functions of the applied Rayleigh number.