Turbulent ocean eddy fluxes are often polluted by the presence of large and rotational components, which are dynamically inert. This suggests that the dynamical influence of ocean eddies should be interpreted by first extracting an underlying dynamically active divergent component, for example via a Helmholtz decomposition. However this decomposition requires the selection of an appropriate boundary condition, and different choices lead to different interpretations of the influence of the eddy fluxes.
Here a decomposition is formulated by noting a relationship between eddy potential vorticity fluxes and eddy momentum forcing. Boundary conditions for the momentum equation can then be used to form a boundary condition for the eddy potential vorticity flux decomposition. The resulting approach has an intuitive physical interpretation, and is equivalent to the solution of an optimisation problem.