A Comparison of the Weakly Nonlinear Instability of Westerly and Easterly Jets in a Two-Layer Beta-Plane Model

Abstract

The nonlinear evolution of disturbances that emanate from unstable westerly and easterly jet profiles is examined with a two-layer quasi-geostrophic ?-plane channel model. Significant differences arise between the solutions for westerly and easterly jets. For unstable narrow (width less than the deformation radius) westerly jets, the disturbance undergoes a sequence of life cycles characterized by barotropic growth and barotropic decay. Unstable easterly jets also give rise to a series of life cycles in which the disturbance grows and decays in a combined baroclinic/barotropic manner. In each of these cases, the disturbance structure remains close to its unstable normal mode form throughout the life cycle. This contrasts with earlier results of Feldstein and Held who find that disturbances emanating from unstable wide (width greater than the deformation radius) westerly jets undergo a change in meridional structure, enhanced lateral radiation, and a single life cycle consisting of baroclinic growth followed by barotropic decay. The wave propagation characteristics of the westerly and easterly jets are examined in the context of linear WKB theory. It is found that the modes growing in the narrow westerly and easterly jets are reflected at turning latitudes. On the other hand, the modes of the unstable wide westerly jet are completely absorbed at critical latitudes. These properties at the bounding latitudes are used to explain differences in the life cycles. The life cycles for westerly and easterly jets are also examined with a forced dissipative model. For both narrow westerly and easterly jets, the disturbance always evolves to a steady state. This contrasts with the multiple life cycle solutions of the wide westerly jet. Finally, the results in this study are related to the nonlinear instability of various jets in the atmosphere.