Vertical Structure of Potential Vorticity Fluxes in Weakly ( and Strongly ) Unstable Flows

Eddying flow in the ocean develops as a result of baroclinic instability, and the environment in which the flow develops is vertically and horizontally inhomogeneous. A theory that takes into account the vertical inhomogeneities and predicts the magnitude and structure of the eddy potential vorticity flux for strongly baroclinically unstable mean shears is reviewed and extended to include the full range of supercriticalities. The theory applies equally to systems with uniform and nonuniform stratification and utilizes the neutral stratification modes and the projection of the mean shear onto these modes. For both strongly and weakly unstable shears, the predicted eddy potential vorticity flux automatically conserves momentum. In the weakly unstable case this result is non-trivial; because β contributes non-negligibly to the mean potential vorticity gradient, the potential vorticity flux can no longer be simply proportional, at each level, to the vortex-stretching part of the potential vorticity gradient and still conserve momentum.