Nonlinear saturation of baroclinic instability in two-layer models

Abstract

The problem of nonlinear saturation of baroclinic waves in two-layer models is studied and it is shown that Shepherd's rigorous bound on the wavy disturbance growth due to instabilities of parallel shear flow can be improved significantly, in some cases, by exact calculation of the averaged Arnol'd's invariant. Shepherd's bound for the Phillips' β-plane two-layer model with constant potential vorticity gradient is achieveable at the minimum critical shear as the supercriticality parameter ε→0. The underlying reason for such an achievable bound for the wavy disturbance is that the condition leading to the Arnol'd's stability theorem is both necessary and sufficient. Based on such an achievable bound (2β/3F)1/2 is deduced as the maximum wave amplitude at the minimum critical shear as the supercriticality parameter ε→0. -from Authors