A Simple Model for the Baroclinic Life Cycle of Meridionally Elongated Eddies in Uniform Shear

Abstract

A highly simplified model for the wave?mean flow interaction in a baroclinic wave life cycle is derived from the quasigeostrophic two-layer system. The simplification is based on a sheared disturbance embedded in a zonal mean flow with uniform vertical and meridional shear. This system, referred to as the uniform shear model, can only be justified in the limit of large meridional eddy elongation. However, the model captures well-known features of baroclinic wave life cycles. These include the excitation of a baroclinic growth and a barotropic decay phase where the zonal mean flow is effectively stabilized by the barotropic governor effect. This effect is a consequence of a nonlinear tilting instability where enstrophy is driven to decreasing scales while the kinetic energy is transformed into the zonal mean barotropic shear flow. A detailed examination of the uniform shear model reveals that the wave evolution depends sensitively on the initial barotropic shear, wave amplitude, and wave tilt. The predictions of the uniform shear model are compared with simulations performed with a high-resolution two-layer model. A high agreement between both models is found in the baroclinic growth stage of the life cycle. The solutions of the high-resolution model begin to deviate after the baroclinic growth ceases. The deviation is largest for weak initial shear where the wave decays rapidly into multiple zonal jets. For moderate initial shear the deviation remains small beyond the equilibration stage in the center part of the channel while near the boundaries secondary disturbances already develop toward the channel center.