The Impact of Abyssal Hill Roughness on the Benthic Tide

The flow of tides over rough bathymetry in the deep ocean generates baroclinic motion including internal waves and bottom‐trapped tides. The stresses generated by this motion feedback on the amplitude and phase of the large‐scale tide. Quantifying the stresses associated with tidal flow over abyssal hills is especially important, as this scale of bathymetry is often unresolved in global baroclinic tide models, and the stresses must therefore be parameterized. Here, we extend the previous theoretical work of the authors to determine the amplitude, phasing, and vertical location of the stresses exerted on a flow driven by a time‐periodic body force when it encounters rough bathymetry. The theory compares favorably with a suite of fully nonlinear numerical simulations. It is shown that all topographic stresses are applied directly above the bathymetry, leading to a two‐layer baroclinic flow, with the near‐bottom spatial‐mean flow (the benthic tide) strongly modified by topographic stresses, and the flow at height unperturbed by the presence of topography. Our results provide a framework to improve baroclinic tide models by (i) providing a simple parameterization for the subinertial stress which is currently not included in any models, (ii) establishing that parameterized stresses should be applied in the diffusive boundary layer directly above the topography, independent of where internal tides may dissipate, and (iii) identifying a minimum resolution of ∼10 km for baroclinic tidal models to adequately capture wave resonance effects that can significantly impact the magnitude of the benthic tide.