Baroclinic instability in the generalized Phillips’ model Part I: Two-layer model

Abstract

The nonlinear stability of the three—layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For comparison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, Β parameter and curvature in vertical profile of the horizontal velocity on the linear instability are discussed by use of the growth rate curves. The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenomenon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form.