Evaluation of the Momentum Closure Schemes in MPAS-Ocean

Abstract

In order to compare and evaluate the performances of the Laplacian viscosity closure, the biharmonic viscosity closure, and the Leith closure momentum schemes in the MPAS-Ocean model, a variety of physical quantities, such as the relative reference potential energy (RPE) change, the RPE time change rate (RPETCR), the grid Reynolds number, the root mean square (RMS) of kinetic energy, and the spectra of kinetic energy and enstrophy, are calculated on the basis of results of a 3D baroclinic periodic channel. Results indicate that: 1) The RPETCR demonstrates a saturation phenomenon in baroclinic eddy tests. The critical grid Reynolds number corresponding to RPETCR saturation differs between the three closures: the largest value is in the biharmonic viscosity closure, followed by that in the Laplacian viscosity closure, and that in the Leith closure is the smallest. 2) All three closures can effectively suppress spurious dianeutral mixing by reducing the grid Reynolds number under sub-saturation conditions of the RPETCR, but they can also damage certain physical processes. Generally, the damage to the rotation process is greater than that to the advection process. 3) The dissipation in the biharmonic viscosity closure is strongly dependent on scales. Most dissipation concentrates on small scales, and the energy of small-scale eddies is often transferred to large-scale kinetic energy. The viscous dissipation in the Laplacian viscosity closure is the strongest on various scales, followed by that in the Leith closure. Note that part of the small-scale kinetic energy is also transferred to large-scale kinetic energy in the Leith closure. 4) The characteristic length scale L and the dimensionless parameter Г in the Leith closure are inherently coupled. The RPETCR is inversely proportional to the product of Г and L. When the product of Г and L is constant, both the simulated RPETCR and the inhibition of spurious dianeutral mixing are the same in all tests using the Leith closure. The dissipative scale in the Leith closure depends on the parameter L, and the dissipative intensity depends on the parameter Г. 5) Although optimal results may not be achieved by using the optimal parameters obtained from the 2D barotropic model in the 3D baroclinic simulation, the total energies are dissipative in all three closures. Dissipation is the strongest in the biharmonic viscosity closure, followed by that in the Leith closure, and that in the Laplacian viscosity closure is the weakest. Mesoscale eddies develop the fastest in the biharmonic viscosity closure after the baroclinic adjustment process finishes, and the kinetic energy reaches its maximum, which is attributed to the smallest dissipation of enstrophy in the biharmonic viscosity closure. Mesoscale eddies develop the slowest, and the kinetic energy peak value is the smallest in the Laplacian viscosity closure. Results in the Leith closure are between that in the biharmonic viscosity closure and the Laplacian viscosity closure.