Environmental Science and Engineering Seminar

Within the next couple of years we expect the resolution of many IPCC-class ocean models to increase to values around 1/4 degree. At this resolution models can produce eddy-like disturbances, but can still not properly resolve eddies at all relevant scales. Adequate parameterizations representing sub-grid eddy effects are thus necessary. Most eddy permitting models presently employ some kind of hyper-viscosity, which in the ``eddy-permitting" regime causes a significant amount of energy dissipation. However, higher resolution simulations show that only enstrophy, but almost no energy, should be dissipated at scales below the grid-scale. As a result of the artificial energy sink associated with viscous parameterizations, the eddy fields in eddy permitting models are typically not energetic enough.

To overcome this problem, we propose a class of sub-grid parameterizations which dissipate enstrophy but not energy. The idea is relatively simple: a standard hyperviscous closure is combined with some mechanism to return the dissipated energy to the resolved flow. Energy is conserved by construction, while enstrophy is dissipated because the energy is returned at larger scales. Two simple ways to return the energy are proposed: one using a stochastic excitation and one using a negative Laplacian viscosity. Both approaches are tested in an idealized model. Either approach is shown to greatly improve the solutions in simulations with typical eddy-permitting resolutions.