Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size

A non-hydrostatic terrain-following model in cross sectional form is applied to study the processes in the lee of a sill in an idealized stratified fjord during super-critical tidal inflow. A sequence of numerical studies with horizontal grid sizes in the range from 100 to 1.5625 m are performed. All experiments are repeated using both hydrostatic and non-hydrostatic versions of the model, allowing a systematic study of possible non-hydrostatic pressure effects and also of the sensitivity of these effects to the horizontal grid size. The length scales and periods of the internal waves in the lee of the sill are gradually reduced and the amplitudes of these waves are increased as the grid size is reduced from 100 down to 12.5 m. With a further reduction in grid size, more short time and space scale motions become superimposed on the internal waves. Associated with the internal wave activity, there is a deeper separation point that is fairly robust to all parameters investigated. Another separation point nearer to the top of the sill appears in the numerical results from the high-resolution studies with the non-hydrostatic model. Associated with this shallower separation point, an overturning vortex appears in the same set of numerical solutions. This vortex grows in strength with reduced grid size in the non-hydrostatic experiments. The effects of the non-hydrostatic pressure on the velocity and temperature fields grow with reduced grid size. In the experiments with horizontal grid sizes equal to 100 or 50 m, the non-hydrostatic pressure effects are small. For smaller grid sizes, the time mean velocity and temperature fields are also clearly affected by the non-hydrostatic pressure adjustments.