The viscous lee wave problem and its implications for ocean modelling

Abstract

Ocean circulation models employ horizontal viscosity and diffusivity to represent unresolved sub-gridscale processes such as breaking internal waves. Computational power has now advanced sufficiently to permit regional ocean circulation models to be run at sufficiently high (100m-1km) horizontal resolution to resolve a significant part of the internal wave spectrum. Here we develop theory for boundary generated internal waves in such models, and in particular, where the waves dissipate their energy. We focus specifically on the steady lee wave problem where stationary waves are generated by a large-scale flow acting across ocean bottom topography. We generalise the energy flux expressions of Bell (1975) to include the effect of horizontal viscosity and diffusivity. Applying these results for realistic parameter choices we show that in the present generation of models with O(1)m2 s −1 horizontal viscosity/diffusivity boundary-generated waves will inevitably dissipate the majority of their energy within a few hundred metres of the boundary. This dissipation is essentially spurious since it is a direct consequence of the artificially high viscosity/diffusivity used in the numerical models and hence caution is necessary in comparing model results to ocean observations. Our theory further predicts that O(0.01)m2 s −1 horizontal viscosity/diffusivity is required to satisfactorily reduce the spurious dissipation and enable a realistic representation of wave dynamics in ocean models Show more