SEAMOUNT CASE
This problem involves the pressure gradient errors that may result in certain numerical treatments for stratified flow near steep bathymetry.
Ideally, a fluid with a level vertical density stratification, initially at rest and unforced, should continue to remain so indefinitely in time. However this property may not be preserved, due to numerical errors associated with the numerical discretization of the horizontal pressure gradient terms if the vertical coordinate system differs from a simple geopotential (z-coordinate) system.
Hence, in order to examine pressure gradient errors, the flow around a tall seamount is examined where the flow is initially at rest and where the density is stratified in the vertical according to a known relation. Schematic plots of a typical -grid and a vertical density stratification for this problem are shown below.
