Absolutely Unstable and Stochastically Forced Baroclinic Waves.

The dynamics of absolutely unstable and stochastically forced eddies are examined in a quasi-geostrophic two-layer model. The concepts of absolute, convective, and spatial instability are reviewed and a new analysis technique for examining these instabilities is presented. The key to understanding the mechanism by which absolute instabilities equilibrate is recognition that linear absolute instabilities can be stabilized by both a reduction of the mean baroclinic shear and by enchancement of the mean barotropic velocity. Numerical studies suggest that if an equilibrated absolute instability were to occur in midlatitudes, a zonal band of surface easterlies exceeding 9000 km would be required and the associated enhanced variances would not be found coincident with the regions of absolute instability. We examine the alternative hypothesis that the transient eddies can be understood as a linear response to stochastic forcing. Closed form expressions for the ensemble average variance and heat flux of the stochastically forced two-layer model are derived. The maintained variance of stochastically forced barotropic jets are enhanced compared to the variance expected in normal systems with identical modal damping rates. We examine quasilinear equilibration of the two -layer model in which the induced eddy fluxes of the stochastically forced zonal mean flow (with fixed forcing amplitude) together with the thermal driving and frictional dissipation are used to force the zonal mean flow toward equilibrium. A general circulation qualitatively similar to that which is observed in the atmosphere is obtained with approximately the same northward heat flux. For sufficiently strong thermal driving the equilibrium cross-channel temperature difference is marginally subcritical and independent of the magnitude of thermal relaxation and stochastic forcing. Although it yields approximately the same state as baroclinic adjustment, this stochastic equilibration mechanism operates on a fundamentally different principal. The quasilinear equilibration is compared with the fully nonlinear equilibration in the final section and implications of these results to understanding the maintenance of variance in quasi-geostrophic systems are discussed.