Stable split time stepping schemes for large-scale ocean modeling

An explicit time integration of the primitive equations, which are often used for numerical ocean simulations, would be subject to a short time step limit imposed by the rapidly varying external gravity waves. One way to make this time step limit less onerous is to split the primitive equations into a simplified two-dimensional set of equations that describes the evolution of the external gravity waves and a much more slowly evolving three-dimensional remainder. The two-dimensional barotropic equations can be rapidly integrated over a large number of short time steps, while a much longer time step can be used with the much more complicated remainder. Unfortunately, it has recently been demonstrated that an inexact splitting into the fast and slow equations can lead to instability in the explicit integration of the slow equations. Here a more exact splitting of the equations is proposed. The proposed spl it time stepping scheme is demonstrated to be stable for linear inertia-gravity waves, subject to a time step limit based on the inertial frequency and internal gravity wave speeds. (C) 1997 Academic Press.