The Nonlinear Dynamics of Slightly Supercritical Baroclinic Jets

Abstract

The nonlinear dynamics of a slightly unstable baroclinic wave is studied for a two-layer f-plane system in which the basic flow is strongly sheared in the horizontal direction. The basic flow is purely baroclinic, i.e., equal and opposite in each layer. In addition, the basic flow vanishes on the channel walls containing the flow. Weakly nonlinear theory predicts that for small supercriticality, the basic wave eigenfunction has the same horizontal structure as the basic flow although it is vertically barotropic. Moreover, weakly nonlinear theory predicts growth of the wave amplitudes, which is unrestrained by wave?mean flow interaction. This prediction is verified by direct numerical calculation. The numerical calculations further reveal the manner by which the wave eventually equilibrates. The strongly growing wave cascades energy to higher zonal harmonics. These harmonics alter the meridional structure of the fundamental that allows wave?mean flow interaction to operate, leading finally to equilibration. If the cascade to higher zonal wavenumbers is artificially blocked by truncating the numerical model to a single zonal wavenumber, equilibration artificially requires the annihilation of the basic shear.