A higher order discontinuous Galerkin, global shallow water model: Global ocean tides and aquaplanet benchmarks

The paper includes a detailed development of the mathematical and numerical framework which is first tested in the context of analyses of a series of well established aquaplanet benchmarks for the shallow water equations on the sphere. These benchmarks include: (1) steady state nonlinear geostrophic flow in the context of an hp convergence study, (2) Rossby wave response arising from a geostrophic flow impinging on localized topography and (3) development of barotropic instability in a perturbed balanced zonal flow. For our target tidal applications the basic shallow water system is extended to include the influence of internal tide-related drag in the deep ocean as well as the drag in shallow marginal seas together with the influence of gravitational self-attraction and loading. Global tidal simulations with various offshore and coastal resolutions are compared with the standard benchmark based upon satellite altimetry data. Initial investigations of the M2 tidal amplitude, phase and energy budget are provided and shown to be highly satisfactory at the level of resolution for which results are provided.