On the linear and weakly nonlinear theory of the barotropic stability of the Bickley jet

Abstract

In this thesis, we study the barotropic stability of the Bickley jet on the $beta$-plane in the context of the linear and weakly nonlinear theory.In the linear theory, the normal mode approach is used where we introduce a small wavelike perturbation to the mean parallel flow to obtain the Rayleigh-Kuo equation. Together with its boundary conditions, this equation is solved as an eigenvalue problem. As a result, new linear unstable sinuous modes are obtained within the narrow region bounded by two known neutral modes. We also locate a sinuous neutral mode which is singular and radiating, near the stability limit of $beta=-2$.An integral part of the thesis involves the application of the weakly nonlinear theory. The temporal evolution of the perturbation amplitude about the varicose neutral mode is studied by means of the Landau equation. Consequently, the value of the Landau constant is deduced which indicates a frequency reduction to the linear perturbation