A SPECTRAL FILTERING PROCEDURE FOR EDDY-RESOLVING SIMULATIONS WITH A SPECTRAL ELEMENT OCEAN MODEL

The numerical simulation of turbulent oceanic flows is susceptible to the appearance of instabilities associated with the misrepresentation of nonlinear interactions among small-scale motions, Specialized filte rs and differencing schemes have been successfully used in the past to suppress the growth of these instabilities in finite-difference ocean models. Here, we introduce a new-filtering procedure designed to cont rol the growth of nonlinear instabilities in the spectral element solu tion of nonlinear oceanic flows. The new procedure involves two separa te steps, First, a spectral filter is applied to the vorticity and div ergence fields to damp oscillations in high-gradient regions and to re store spectral accuracy away from them. Second, the associated velocit y field is computed from a set of Poisson equations, and its boundary conditions and interelement continuity are restored. This two-step str ategy avoids the loss of C-0 continuity and the weakening of Dirichlet boundary conditions that can result when the filter is directly appli ed to the velocity field. The behavior of the filter is investigated n umerically an the canonical problem of the double-gyre wind-driven cir culation in a rectangular basin using a spectral element shallow water model. The parameters of the simulation are chosen to produce mesosca le eddies. The filter is able to stabilize the simulation even at coar se resolution and to recover the ''correct'' statistical behavior with as few as two grid points per Rossby deformation radius, Finally, a s imulation of the wind-driven circulation in the North Atlantic Ocean i s performed to illustrate the effectiveness of the filter in realistic settings. (C) 1997 Academic Press.