| Abstract: Ocean simulations are in part determined by topographic
waves with speeds and spatial scales dependent on bottom slope. By their
very nature, discrete z-level ocean models
have problems accurately representing bottom topography when slopes are
less than the grid cell aspect ratio delta z/delta x.
In such regions, the dispersion relation for topographic waves is inaccurate.
However, bottom topography can be accurately represented in discrete z-level
models by allowing bottom-most grid cells to be partially filled with land.
Consequently, gently sloping bottom topography is resolved on the scale
of horizontal grid resolution and the dispersion relation for topographic
waves is accurately approximated. In contrast to the standard approach
using full cells, partial cells imply that all grid points within a vertical
level are not necessarily at the same depth and problems arise with pressure
gradient errors and the spurious diapycnal diffusion. However, both problems
have been effectively dealt with. Differences in flow fields between simulations
with full cells and partial cells can be significant, and simulations with
partial cells are more robust than with full cells. Partial cells provide
a superior representation of topographic waves when compared to the standard
method employing full cells. |