  Although the two-layer quasi-geostrophic equations (2QGE) are a simplified
model for the dynamics of a stratified, wind-driven ocean, their numerical
simulation is still plagued by the need for high resolution to capture the full
spectrum of turbulent scales. Since such high resolution would lead to
unreasonable computational times, it is typical to resort to coarse
low-resolution meshes combined with the so-called eddy viscosity
parameterization to account for the diffusion mechanisms that are not captured
due to mesh under-resolution. We propose to enable the use of further coarsened
meshes by adding a (linear or nonlinear) differential low-pass to the 2QGE,
without changing the eddy viscosity coefficient. While the linear filter
introduces constant (additional) artificial viscosity everywhere in the domain,
the nonlinear filter relies on an indicator function to determine where and how
much artificial viscosity is needed. Through several numerical results for a
double-gyre wind forcing benchmark, we show that with the nonlinear filter we
obtain accurate results with very coarse meshes, thereby drastically reducing
the computational time (speed up ranging from 30 to 300).
