Nonlinear Baroclinic Instability on the Sphere: Multiple Life Cycles with Surface Drag and Thermal Damping

Abstract

A multilevel, global, primitive equation model is used to examine the nonlinear development of baroclinic waves (confined initially to a single zonal wavenumber) on a symmetric zonal flow. The focus is on the influence of highly simplified surface drag and thermal damping on the evolution of the flow beyond an initial eddy life cycle. Without surface drag and thermal damping and with relatively weak internal diffusion, it is found that multiple life cycles occur in the evolution to an essentially wave-free state. With stronger diffusion, only a single life cycle characterized by baroclinic growth and barotropic decay is obtained. The life cycles that follow the initial cycle with weak diffusion are strongly barotropic, entailing barotropic growth and decay. The episodes of barotropic growth are associated with wave radiation, wave breaking, and overreflection on the equatorward flanks of the jet near a critical surface. With strong diffusion, the potential vorticity mixing associated with the breaking is reduced considerably, and significant barotropic growth (and overreflection) does not occur. In all the simulations without drag and damping, the “barotropic governor” identified by James and Gray is primarily responsible for the stabilization of the mean flow in the final wave-free state. Repeated life cycles characterized largely by baroclinic growth and barotropic decay are obtained with the simplified surface drag and thermal damping. Significant barotropic growth occurs in the early stages of most of the life cycles, associated with wave breaking and overreflection on the equatorward side of the jet. Multiple life cycles of baroclinic growth and barotropic decay occur in the complete absence of thermal damping (though damping is certainly necessary for sustained life cycles), demonstrating the crucial role of surface drag in suppressing the barotropic governor. With thermal damping but without surface drag, the evolution is similar to that without both drag and damping in being highly barotropic. The simulations with surface drag and thermal damping are compared with observations of medium-scale baroclinic waves in Southern Hemisphere summer and are found to be very similar.