Quote from: https://ui.adsabs.harvard.edu/abs/2005CSR....25..829B/abstract

  Sigma coordinate ocean models, or models based on more generalised topography following coordinate systems, are presently widely used in oceanographic studies. Terrain following models are attractive because of their abilities to resolve the surface and bottom layers. However, the internal pressure gradient estimation is problematic in such models, and artificial pressure gradients may create artificial flow. In fine resolution studies where topography and stratification is well resolved, the artificial flow due to erroneous pressure gradients is small because the errors typically converge to zero with the square of the grid size. In coarse resolution studies, however, there may still be large erroneous pressure gradients that may create strong artificial flow. To avoid this, larger horizontal viscosities than one would like to apply from physical considerations, are applied in most studies so far. This means that smaller scale phenomena in the flow will be poorly represented. The response of the flow to the pressure errors in long time simulations with low horizontal viscosity is very important. In this study it is demonstrated that the choice of the time stepping method may affect the growth of the erroneous flow considerably. Increasing the implicit nature of the time stepping method, will generally reduce the growth. Recently many oceanic model studies have been performed with models that allow non-hydrostatic pressure effects. In the present study it is shown that when allowing the flow to adjust to non-hydrostatic pressure, the growth of the flow due to internal pressure errors may be strongly affected.