The structure of baroclinic turbulence in an idealized family of baroclinically-unstable flows

We present and investigate the nonlinear equilibrated states of a two-parameter family of idealized local mean flows that capture the primary mesoscale baroclinic instability types found in the world's oceans. The model flow yields a mean potential vorticity (PV) gradient that consists of baroclinic part, equal to the stretching term from the baroclinic shear, and a depth-averaged part, equal to the sum of beta and the stretching associated with lateral buoyancy gradients at the ocean's surface. The model may be susceptible to Phillips-type baroclinic instability, arising from sign changes in the baroclinic PV gradient, Charney-type instability, which occurs when the surface buoyancy gradient has the opposite sign of the barotropic PV gradient, or both (and may be stable for a narrow slice of parameter space). The two instability types (which may occur alone or in the same flow) lead to distinct turbulent states and eddy fluxes. In some instances, the equilibrated flow exhibits a transition scale below which energetic submesoscale flows develop, displaying features that bear resemblance to Surface Quasigeostrohphic (SQG) turbulence. When such flows result from a Charney-type instability, however, the submesoscale range is non-inertial, being forced at all scales by submesoscale instabilities (akin to, but weaker than Mixed Layer Instabilities). These flows also exhibit a turbulent 'boundary layer,' with a thickness given roughly by the Charney depth scale from the associated linear instability problem. The detailed structure of the turbulence resulting from this family of mean flows provides a useful simplified model for the regional variation of eddy structure in the global ocean.