Evaluating and improving wave and non-wave stress parametrisations for oceanic flows

Whenever oceanic currents flow over rough topography, there is an associated stress that acts to modify the flow. In the deep ocean, this stress is predominantly a form drag due to pressure differentials across topography, caused by the formation of internal waves and other baroclinic motions: processes that act on such small scales most global ocean models cannot resolve. Despite the need to incorporate this stress into ocean models, existing parametrisations are limited in their applicability. For instance, most parametrisations are only suitable for small-scale topography and are either for periodic or steady flows, but rarely a combination thereof. Here we summarise some of the most widely used parametrisations and evaluate the accuracy of a carefully selected subset using hundreds of idealised two-dimensional and three-dimensional simulations spanning a wide parameter space. We focus on the case of an isolated Gaussian hill as an idealised representation of a seamount. In cases where the parametrisations prove to be inaccurate, we use our data to suggest improved formulations. Our results thus provide a starting point for a comprehensive parameterisation of topographic stresses in ocean models where fine scale topography is unresolved.