Eddy viscosity and hyperviscosity in spectral simulations of 2D drift wave turbulence

A wavenumber dependent eddy viscosity is calculated for a simple two-dimensional drift wave model from direct numerical simulations for a wide range of parameters and cutoff wavenumber. The damping rate given by this eddy viscosity is well modeled by a hyperviscosity, where the power and magnitude are parameterized as functions of the shear in the resolved advecting velocity. Tests in simulations with low resolution find that the use of this parameterized hyperviscosity yields somewhat better results than the use of hyperviscosity with fixed power and is significantly better the use of no extra damping term or a Smagorinsky type eddy viscosity. This parameterized hyperviscosity is very useful computationally, since reducing resolution requirements by even a factor of 2 reduces the computational requirements by a factor of 8 in two dimensions, or 16 in three dimensions.