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

Abstract: 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.