An Energy- and Enstrophy-Constrained Parameterization of Barotropic Eddy Potential Vorticity Fluxes

Abstract A parameterization for barotropic eddy potential vorticity (PV) fluxes is introduced, which applies both an energetic and an enstrophetic constraint to a downgradient PV mixing closure. An eddy kinetic energy budget and an eddy potential enstrophy budget are employed to constrain the parameterized eddy PV fluxes. Through the budgets, the parameterization facilitates a bidirectional exchange of kinetic energy between the parameterized eddies and the large-scale flow and a conversion of potential enstrophy from the large-scale flow to the parameterized eddies. The parameterization is tested in simulations of barotropic, freely decaying turbulence in a doubly periodic domain over variable bottom topography. The simulations show that employing the parameterization results in an upscale transfer of kinetic energy on average, consistent with quasigeostrophic theory. Furthermore, the kinetic energy and potential enstrophy budgets employed are sufficient to constrain the large-scale flow in a realistic manner when compared to an eddy-resolving model. As a result, a topography-following flow of the correct magnitude emerges in a coarse-resolution model with parameterized eddy effects. Dissipation in the coarse-resolution simulations is significant, leading to the most significant source of discrepancy between the coarse-resolution simulation with parameterized eddy effects and the eddy-resolving simulation. This work constitutes a first step toward the ultimate aim of parameterizing both baroclinic and barotropic turbulence. How this may be achieved by integrating this parameterization with other methods in more realistic ocean simulations is discussed. Significance Statement Mesoscale eddies in the ocean, the analog 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 toward a structure which resembles that of the ocean floor. Commonly employed methods of representing eddies in climate models are unable to capture this process because they fail to represent accurately the underlying physical processes that constrain the eddies. Here, we present a method for representing ocean eddies in climate models, which uses the 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, analyzing both the parameters that are important in the underlying physics and the properties of the large-scale flows produced by the eddies.