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Internal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially averaged kinetic energy and dissipation of even highly nonlinear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes. [ABSTRACT FROM AUTHOR]

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. Plain Language Summary: The ocean tide is a periodic motion of the water column at the scale of ocean basins. The amplitude of the ocean tide is determined by a balance between the gravitational attraction of the moon and the forces exerted when the tide flows over the rough seafloor. Much of the roughness in the deep ocean is due to mountains on the seafloor, 10–50 km in width, known as "abyssal hills." In this study, mathematical descriptions are developed for the strength and distribution of the forces exerted on the ocean tide due to its interaction with these hills. These forces always act below the crest of the hills, leading to a sub‐crest or "benthic tide" that differs from the tide above the crest of the hills. Our results provide a framework for improving the representation of tides in numerical ocean models. Key Points: The interaction of the spatial‐mean tide with rough bathymetry generates baroclinic motion including internal tidesThese motions exert stresses on the spatial‐mean tide near the seafloor which modifies the benthic tidal amplitudeThe benthic tidal amplitude may be decreased or increased depending on the nature of the interaction [ABSTRACT FROM AUTHOR]

The action of the barotropic tide over seafloor topography is the major source of internal waves at the bottom of the ocean. This internal tide has long been recognized to play an important role in ocean mixing. Here it is shown that the internal tide is also associated with a net (domain integrated) momentum flux. The net flux occurs as a result of the Doppler shifting of the internal tide at the point of generation by near-bottom mean flows. Linear theory is presented that predicts the amplitude of the wave momentum flux. The net flux scales with the bottom flow speed and the topographic wavenumber to the fourth power and is directed opposite to the bottom flow. For realistic topography, the predicted peak momentum flux occurs at scales of order 10 km and smaller, with magnitudes of order 10−3–10−2 N m−2. The theory is verified by comparison with a suite of idealized internal wave-resolving simulations. The simulations show that, for the topography considered, the wave momentum flux radiates away from the bottom and enhances mean and eddying flow when the tidal waves dissipate in the upper ocean. Our results suggest that internal tides may play an important role in forcing the upper ocean. [ABSTRACT FROM AUTHOR]