Equilibrium statistical predictions for baroclinic vortices: The role of angular momentum

We develop a point-vortex equilibrium statistical model for baroclinic quas igeostrophic vortices within the context of a two-layer quasigeostrophic fl uid that evolves in all of space. Angular momentum, which follows from the rotational symmetry of the unbounded domain, is the key conserved quantity, introducing a length scale that confines the most probable states of the s tatistical theory. We apply the theory as a model of localized convection i n a preconditioned gyre. To illustrate this application, the preconditioned cyclonic, largely barotropic gyres are modeled as "zero inverse temperatur e" states, which are explicit solutions to the mean-field equations with a Gaussian probability distribution of vortices. Convection is modeled by a c loud of point-vortex herons - purely baroclinic arrangements of point vorti ces, cyclonic above and anticyclonic below - which capture the short-term, geostrophically balanced response to strong surface cooling. Numerical heto n studies (Legg and Marshall, 1993, 1998) have shown that a preexisting bar otropic rim current can suppress baroclinic instability and confine anomali es of potential vorticity and temperature introduced by the cold-air outbre ak. Here, we demonstrate that the lateral extent of the most probable state s of the statistical theory are constrained by the angular momentum. Withou t resolution of the detailed dynamics, the equilibrium statistical theory p redicts that baroclinic instability is suppressed for preconditioned flows with potential vorticity of the same sign in each layer provided that the s trength of connective overturning does not change the sign of potential vor ticity in one of the layers. This result agrees with detailed simulations ( Legg and Marshall, 1998) and supports the potential use of these statistica l theories as parametrizations for crude closure.