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

Abstract

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 a 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 norms enable 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 alpha-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.

44 pages, 21 figures, 1 Appendix, submitted to Ocean Modeling

References in corpus (6)

• Implementation of the LANS-alpha turbulence model in a primitive equation ocean model
• Highly turbulent solutions of LANS-alpha and their LES potential
• A scale-invariant formulation of the anticipated potential vorticity method
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model
• A hybrid MPI-OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence

Cited by in corpus (6)

• A posteriori learning for quasi-geostrophic turbulence parametrization
• Generative data-driven approaches for stochastic subgrid parameterizations in an idealized ocean model
• Subgrid parameterizations of ocean mesoscale eddies based on Germano decomposition
• Geodesic motion on the groups of diffeomorphisms with $H^1$ metric as geometric generalised Lagrangian mean theory
• Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence
• Evaluation of Analytical Turbulence Closures for Quasi-Geostrophic Ocean Flows with Coastal Boundaries