Abstract
We develop a time discretization framework based on exponential integrators for a stacked rotating shallow-water ocean model. The methods are based on a splitting of the forcing term into a linear rotating multi-layer wave-operator and a non-linear residual, corresponding to the advective forces. We discuss different solution strategies for the linear part by an approximation of the matrix exponential with skew-adjoint Krylov methods. The resulting integrator can take large time steps up to the advective time scale, independent of the speed of internal and external gravity waves. Additionally, the vertically coherent structure of the fastest waves can be used to compress the wave operator into a few vertical modes. In a special case, employing a reduction only to the barotropic component, we obtain a new class of methods with similar features to the well-known split-explicit method. Numerical experiments in the context of the SOMA testcase show that the methods are stable over decade-long simulation horizons and accurately reproduce solution statistics.