A new analytical solution is presented for the case of a stratified seiche. This solution, especially its energetics, is useful for the validation of numerical shallow water models under stratified conditions. The utility of the analytical solution for validation is shown by using it to validate a simple finite difference numerical model. A comparison of the energetics of the numerical and analytical solutions reveals that the model results converge rapidly to the analytical solution with increasing resolution, such that a grid size of 30 630 would appear adequate for validation. In addition to properly resolving the spatial features, good temporal resolution is also necessary for validation, i.e use of a Courant number (Cr) less than one. For example, owing to the numerical dispersion of the present model, using Cr 5/4 rather than Cr 1/4 for the 50 650 grid resulted in 316 times larger RMS errors of model versus analytical barotropic available potential energy.
This new analytical solution should be applied to a test suite of such validation tools before using such numerical models to simulate the more realistic geophysical flows encountered in lakes, bays, harbours and semienclosed seas under stratified conditions.