The influence of an irregular grid upon internal wave propagation

Abstract

A cross-sectional non-linear model of wind induced circulation in a stratified basin of constant depth, neglecting rotational effects, is used to examine the influence of grid resolution upon the accuracy of internal wave propagation. In addition the effect upon the accuracy and stability of the solution on an irregular grid of using a scale selective formulation of horizontal diffusion is considered. The initial response to an along-basin wind impulse is coastal downwelling at the downwind end, with upwelling of heavy water and convective mixing at the upwind end. Subsequently a horizontal density front and associated internal waves propagate away from the coast. Calculations show that the intensity of the horizontal and vertical currents associated with the front depends upon vertical and horizontal eddy viscosity, with intensity and hence horizontal gradient increasing as viscosity decreases. 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.