A framework for the evaluation of turbulence closures used in mesoscale ocean large-eddy simulations

We present a methodology to determine the best turbulence closure for an eddy-permitting ocean model through measurement of the error-landscape of the closure’s subgrid spectral transfers and flux. We apply this method to 6 different closures for forced-dissipative simulations of the barotropic vorticity equation on an f-plane (2D Navier–Stokes equation). Using a high-resolution benchmark, we compare each closure’s model of energy and enstrophy transfer to the actual transfer observed in the benchmark run. The error-landscape norm enables us to both make objective comparisons between the closures and to optimize each closure’s free parameter for a fair comparison. The hyper-viscous closure most closely reproduces the enstrophy cascade, especially at larger scales due to the concentration of its dissipative effects to the very smallest scales. The viscous and Leith closures perform nearly as well, especially at smaller scales where all three models were dissipative. The Smagorinsky closure dissipates enstrophy at the wrong scales. The anticipated potential vorticity closure was the only model to reproduce the upscale transfer of kinetic energy from the unresolved scales, but would require high-order Laplacian corrections in order to concentrate dissipation at the smallest scales. The Lagrangian-averaged α-model closure did not perform successfully for forced 2D isotropic Navier–Stokes: small-scale filamentation is only slightly reduced by the model while small-scale roll-up is prevented. Together, this reduces the effects of diffusion.