An accurate hyperbolic system for approximately hydrostatic and incompressible oceanographic flows

It is well known that severe restrictions on accuracy and stability arise when using a numerical model based on the Eulerian equations to compute the low frequency motions of physical oceanography. We show that the loss of accuracy is due to the extreme skewness of the system. Although the system can be transformed to symmetric hyperbolic form, the diagonal transformation matrix contains factors that produce mathematical estimates indicating loss of accuracy and this occurs in practice. The stability restriction is just a result of the multiple time scales present in the system, i.e. the presence of sound waves. We discuss three alternatives to overcome these restrictions.