Abstract
The stability of finite-amplitude baroclinic waves in a two-layer channel flow is investigated by using the generalized Landau equiation which describes temporal and spatial modulations of finite-amplitude waves in a weakly non-linear regime. We first obtain a plane wave solution of the generalized Landau equation and then examine its stability with respect to sideband perturbations.
A finite-amplitude wave of wavenumber α in a supercritical state is stable if α satisfies the inequality L±2(α±-αc)2>(α-αc)2, where αc;denotes the critical wavenumber at the linearly marginal state while α+ and α-(α+>α-) are wavenumbers on the neutral curve at a prescribed supercritical state. The coefficient L±2 is 1/3 when the beta effect is absent, while it is generally greater than 1/3 when the beta effect is present.
