Evaluating and Improving Wave and Nonwave Stress Parameterizations for Oceanic Flows

Abstract 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 parameterizations are limited in their applicability. For instance, most parameterizations are only suitable for small-scale topography and are either for periodic or steady flows but rarely a combination thereof. Here, we summarize some of the most widely used parameterizations and evaluate the accuracy of a carefully selected subset using hundreds of idealized two-dimensional and three-dimensional simulations spanning a wide parameter space. We focus on the case of an isolated Gaussian hill as an idealized representation of a seamount. In cases where the parameterizations prove to be inaccurate, we use our data to suggest improved formulations. Our results thus provide a starting point for a comprehensive parameterization of topographic stresses in ocean models where fine-scale topography is unresolved. Significance Statement As the ocean flows over topographic features, it experiences a force. Such topography includes undersea mountains that are too small to be accurately described by global ocean and climate models. These forces shape the ocean structure considerably and affect large-scale ocean circulation features, like the Atlantic meridional overturning circulation. Because there is no hope to accurately include these small-scale effects in climate projections, we need expressions (a.k.a. parameterizations) for the collective force they exert on the ocean. Here, we evaluate existing parameterizations for the force created when an oceanic current flows over an underwater hill by comparing them to the output of small-scale, high-resolution ocean simulations. Compared to previous studies, we cover a much wider range of cases. This allows us to see where existing parameterizations break down and also suggests improvements to these parameterizations, taking us closer to the goal of developing a general and widely applicable mathematical description of this phenomenon.