An energy and enstrophy constrained parameterization of barotropic eddy potential vorticity fluxes

A parameterization for barotropic eddy potential vorticity fluxes is introduced which applies both an energetic and an enstrophetic constraint to down-gradient PV mixing.An eddy kinetic energy budget and an eddy potential enstrophy budget are employed to constrain the parameterized eddy PV fluxes.The parameterization is tested for freely-decaying turbulence over variable bottom topography.Results of the simulations show that the parameterization can convert energy from the parameterized eddies to the mean flow.Furthermore, the kinetic energy and potential enstrophy budgets employed are sufficient to constrain the large-scale flow such that no spurious source of energy is introduced.As a result, the parameterization is able to produce a topography-following flow of the correct order of magnitude when compared with a high-resolution simulation.SIGNIFICANCE STATEMENT: Small-scale eddies in the ocean, the analogue of atmospheric weather systems, are an important factor in determining the large-scale flow.In particular, in regions where the height of the ocean floor varies, eddies drive the flow towards a structure which resembles that of the ocean floor.Current methods of representing eddies in climate models are unable to capture the latter process because they fail to represent accurately the underlying physical processes that constrain the eddies.Here we present a new method for representing ocean eddies in climate models which uses conservation of energy, and of a similar quantity that measures the amount of turbulent stirring, to constrain the feedback of the eddies on the large-scale flow.We test the new method experimentally in a simple computational ocean model, analysing both the parameters that are important in the underlying physics and the large-scale flows produced by the eddies.