A two-mode numerical model with applications to coastal upwelling

A continuously stratified, linear two mode numerical model has been developed. The model incorporates a free surface and finite amplitude topography.The vertical dependence in the equations is removed by applying a Galerkin procedure which uses the normal modes as test functions. The vertical structure is therefore determined by the normal modes.In order to find a suitable efficient numerical scheme to solve the equations a fairly general phase and stability analysis is carried out for the one dimensional gravity wave equations. The A.D.I. scheme was found to be the most suitable scheme.The model is applied to coastal upwelling. A number of two dimensional (x, z) experiments have been carried out. The advantage of the two mode model above the two layer models is that considerable detail of the vertical structure is readily obtained and that no difficulties with the intersection of interfaces with the topography or the seasurface are present. A three dimensional (x, y, z) test run was done for a region along the south western coast of Africa. The results of this experiment are discussed.