Numerical studies of internal waves at a sill: Sensitivity to horizontal grid size and subgrid scale closure

A non-hydrostatic terrain following model in cross sectional form is applied to study the generation and propagation of tidally forced internal waves near a sill in an idealized loch. On inflow internal waves are generated behind the sill, and they propagate from the sill. There is a transfer of energy from the barotropic tide to internal waves and then to irreversible mixing. The range of length scales involved goes from the scale of the forced tide to scales associated with wave breaking. This wide range of scales makes it very difficult to resolve all relevant length scales with a numerical model using a uniform finite difference grid. The sensitivity of the numerical results to the grid resolution and the parameterisation of subgrid scale mixing is investigated. Initial calculations are performed with constant values of viscosity and diffusivity, and subsequently they are repeated using large eddy simulations and including Richardson number dependant vertical mixing.In the studies with sub-critical flow over the sill, the results are robust to changes in the grid size. With stronger forcing, the flow over the sill becomes super-critical during maximum inflow, and the frequency and the nature of the internal waves generated in the lee of the sill becomes grid size dependant. For the super-critical case, the solution is sensitive to the subgrid scale closure scheme. Calculations show that with constant and small values of vertical viscosity and diffusivity, strong internal waves are generated on inflow in the lee of the sill. When using Richardson number dependant vertical viscosity and diffusivity, more of the tidal energy goes into vertical irreversible mixing, and less into internal waves.