Eddying flow in the ocean develops as a result of baroclinic instability, and in vertically inhomogeneous environments. The author will review a theory which predicts the magnitude and structure of the resulting potential vorticity for strongly unstable mean shears, and extend its application to weakly unstable flows. The theory applies equally to systems with uniform and non-uniform 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 the Coriolis gradient beta 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.

The proposed theory has implications for eddy parameterization in ocean general circulation models, but can be used directly in the interpretation of ocean data as well. Applications of the theory in both areas will be discussed.