The influence of an irregular grid upon internal wave propagation

Calculations using a range of uniform and variable horizontal grids show the importance of a fine near-coastal grid on the short time scale when the front is formed. With an irregular grid and constant horizontal viscosity physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. However when horizontal viscosity is computed using a Smagorinsky formulation, this acts as a grid size dependent filter and removes the physically unrealistic short internal waves, thereby stabilizing the solution. If the empirical coefficient in the Smagorinsky formulation is too large, excessive smoothing can occur, spoiling the advantages of using an irregular grid. A reduced value of the coefficient reflecting the grid refinement on an irregular grid gave a stable solution without excessive smoothing.