Large Eddy Simulation of the Quasi-Geostrophic Equations of Oceanic Flows

We developed an approximate deconvolution (AD) large eddy simulation (LES) model for the two-layer quasi-geostrophic equations (QGE). The AD closure modeling approach is appealing for geophysical flows because it needs no additional phenomenological approximations to the original equations, and it can achieve high accuracy by employing repeated (computationally efficient and easy to implement) filtering. We applied the AD-LES model to mid-latitude two-layer square oceanic basins, which are standard prototypes of stratified ocean dynamics models. Compared with a high-resolution simulation, AD-LES yielded accurate results at significantly lower computational cost. The sensitivity of the AD-LES results with respect to changes in input parameters was also performed. We discovered that although the AD-LES model was robust with respect to changes in parameters, changing the spatial filter made a huge difference. Two spatial filters were investigated in the AD-LES model: tridiagonal and elliptic differential. We found the tridiagonal filter did not introduce any numerical dissipation in the AD-LES model. The differential filter, however, added a significant amount, and our numerical results show the new AD-LES model used in with the differential filter can be employed successfully on meshes significantly coarser than the Munk scale and with an eddy viscosity coefficient that is dramatically lower than that used in the original two-layer QGE. Although we do not provide a solution to the longstanding quest for finding a rigorous derivation of the eddy viscosity coefficients used in ocean modeling, we put forth a novel approach, serendipitously discovered in our numerical investigation. The main strength of this new approach is that the modeling error can be disentangled from the numerical discretization error and can be studied separately in this framework. This could lead to more robust and general LES models for large scale geophysical flows.