Finite Amplitude Equilibration of Baroclinic Waves on a Jet

A quasi-geostrophic two-layer model is used to study the equilibration of baroclinic waves. In this model, if the background flow is relaxed toward a jet-like flow, a finite amplitude baroclinic wave solution can be realized even in a sub-critical region of the model's parameter space. Analyses of the model equations and numerical model calculations indicate that wave breaking in the upper layer plays a pivotal role for the equilibration process, in two different ways. Firstly, as previously pointed out by Robinson, the wave breaking produces a zonal mean circulation which strengthens the baroclinity at the jet center. However, this effect makes a positive contribution to wave activity production only if the Ekman friction rate is greater than the thermal damping rate. It was also found that the presence of curvature in the lower layer wind does not allow the final equilibrium supercriticality to be greater than that of the radiative equilibrium flow profile. The second effect of the wave breaking is to reduce the impact of thermal damping on the waves. This occurs because the upper layer wave breaking acts to shorten the meridional scale of the upper layer waves, increasing their eastward phase speed. As a result, the waves' vertical phase tilt becomes smaller, thereby weakening the thermal damping effect. Because the meridional shear associated with the jet promotes the occurrence of wave breaking even before the waves reach their critical latitudes, we conclude that it is ultimately the meridional shear that allows for the subcritical instability.