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The method of decomposing surface and internal tides determines the expression for internal tide energy, energy flux, and energy conversion. The de facto standard is to define surface tides as depth-averaged pressure and horizontal velocity and internal tides as the residuals. This decomposition, which is equivalent to projecting motion onto vertical modes that obey a rigid lid, is known to produce spurious energy conversion C S through movement of the free surface. Here, motion is instead projected onto modes that obey a linear, free-surface boundary condition. The free-surface modes are shown to obey a more complicated orthogonality condition than rigid-lid modes but are still straightforward to calculate numerically. The resulting decomposition (i) completely eliminates spurious energy conversion C S and (ii) leads to a more precise expression for topographic internal tide generation C , which now depends on horizontal gradients in the vertical structure of the surface tide. Numerical simulations and rough global estimates indicate that corrections to C are a maximum of a few percent. However, C S produces spurious energy flux divergences/convergences in the open ocean, which are the same order of magnitude [ O (1–10) mW m −2 ] as open-ocean internal tide energy dissipation.

We construct a computationally inexpensive semi‐analytical method to compute the tidal conversion into vertical modes by continental slopes and shelves, and apply it at the global scale. It relies on a vertically two‐dimensional reduced‐physics numerical model and uses the observed bottom topography, ocean stratification, and tidal currents as inputs. The method is applicable no matter how steep the slope is and it resolves the onshore and offshore baroclinic tidal energy fluxes. The output is validated with the conversion diagnosed from a global general circulation model simulation. Plain Language Summary Internal tides are waves generated by tidal currents flowing over rough bottom topography, and propagating in the ocean interior. The energy released by these waves, when they break, directly impacts the background ocean. Among others, it influences the oceanic heat and carbon distribution. Knowing where internal tides break is therefore key to better understanding our climate system. The problem of internal‐tide generation is highly nonlinear, and it is not yet solved for arbitrary topography. However, there exist a few alternatives to the exact mathematical description of the generated waves. Semi‐analytical methods based on linear wave theory represent one such alternative, and have been applied to most of the open ocean. However, linear theory fails completely at the step‐like topography of continental slopes. In this study, we compute the internal‐tide generation occurring at continental slopes, at the global scale, using a reduced‐physics model fed with observations. This conceptually simple model largely reproduces the conversion diagnosed from a full‐blown numerical model simulation. Our results confirm the substantial contribution from continental slopes to the global internal‐tide generation. Moreover, they unveil the modal partitioning of the energy flux in these regions. This is critical to predicting where the waves energy is dissipated. Key Points We construct a semi‐analytical method to compute the tidal conversion into modes 1–5 along continental margins globally The method resolves the onshore and offshore energy fluxes The results compare remarkably well with the conversion diagnosed from a realistic simulation

Internal tides, generated by barotropic tides flowing over rough topography, are a primary source of energy into the internal wave field. As internal tides propagate away from generation sites, they can dephase from the equilibrium tide, becoming nonstationary. Here, we examine how low-frequency quasigeostrophic background flows scatter and dephase internal tides in the Tasman Sea. We demonstrate that a semi-idealized internal tide model [the Coupled-Mode Shallow Water model (CSW)] must include two background flow effects to replicate the in situ internal tide energy fluxes observed during the Tasmanian Internal Tide Beam Experiment (TBeam). The first effect is internal tide advection by the background flow, which strongly depends on the spatial scale of the background flow and is largest at the smaller scales resolved in the background flow model (i.e., 50–400 km). Internal tide advection is also shown to scatter internal tides from vertical mode-1 to mode-2 at a rate of about 1 mW m −2 . The second effect is internal tide refraction due to background flow perturbations to the mode-1 eigenspeed. This effect primarily dephases the internal tide, attenuating stationary energy at a rate of up to 5 mW m −2 . Detailed analysis of the stationary internal tide momentum and energy balances indicate that background flow effects on the stationary internal tide can be accurately parameterized using an eddy diffusivity derived from a 1D random walk model. In summary, the results identify an efficient way to model the stationary internal tide and quantify its loss of stationarity.

Packets of nonlinear internal waves (NLIWs) in a small area of the Mid-Atlantic Bight were 10 times more energetic during a local neap tide than during the preceding spring tide. This counterintuitive result cannot be explained if the waves are generated near the shelf break by the local barotropic tide since changes in shelfbreak stratification explain only a small fraction of the variability in barotropic to baroclinic conversion. Instead, this study suggests that the occurrence of strong NLIWs was caused by the shoaling of distantly generated internal tides with amplitudes that are uncorrelated with the local spring-neap cycle. An extensive set of moored observations show that NLIWs are correlated with the internal tide but uncorrelated with barotropic tide. Using harmonic analysis of a 40-day record, this study associates steady-phase motions at the shelf break with waves generated by the local barotropic tide and variable-phase motions with the shoaling of distantly generated internal tides. The dual sources of internal tide energy (local or remote) mean that shelf internal tides and NLIWs will be predictable with a local model only if the locally generated internal tides are significantly stronger than shoaling internal tides. Since the depth-integrated internal tide energy in the open ocean can greatly exceed that on the shelf, it is likely that shoaling internal tides control the energetics on shelves that are directly exposed to the open ocean.

Observations from Eel Canyon, located on the north coast of California, show that elevated turbulence in the full water column arises from the convergence of remotely generated internal wave energy. The incoming semidiurnal and bottom-trapped diurnal internal tides generate complex interference patterns. The semidiurnal internal tide sets up a partly standing wave within the canyon due to reflection at the canyon head, dissipating all of its energy within the canyon. Dissipation in the near bottom is associated with the diurnal trapped tide, while midwater isopycnal shear and strain is associated with the semidiurnal tide. Dissipation is elevated up to 600 m off the bottom, in contrast to observations over the flat continental shelf where dissipation occurs closer to the topography. Slope canyons are sinks for internal wave energy and may have important influences on the global distribution of tidally driven mixing.

Mode-1 internal tides can propagate far away from their generation sites, but how and where their energy is dissipated is not well understood. One example is the semidiurnal internal tide generated south of New Zealand, which propagates over a thousand kilometers before impinging on the continental slope of Tasmania. In situ observations and model results from a recent process-study experiment are used to characterize the spatial and temporal variability of the internal tide on the southeastern Tasman slope, where previous studies have quantified large reflectivity. As expected, a standing wave pattern broadly explains the cross-slope and vertical structure of the observed internal tide. However, model and observations highlight several additional features of the internal tide on the continental slope. The standing wave pattern on the sloping bottom as well as small-scale bathymetric corrugations lead to bottom-enhanced tidal energy. Over the corrugations, larger tidal currents and isopycnal displacements are observed along the trough as opposed to the crest. Despite the long-range propagation of the internal tide, most of the variability in energy density on the slope is accounted by the spring–neap cycle. However, the timing of the semidiurnal spring tides is not consistent with a single remote wave and is instead explained by the complex interference between remote and local tides on the Tasman slope. These observations suggest that identifying the multiple waves in an interference pattern and their interaction with small-scale topography is an important step in modeling internal energy and dissipation.

The linear transfer of tidal energy from large to small scales is quantified for small tidal excursion over a near-critical continental slope. A theoretical framework for low-wavenumber energy transfer is derived from “flat bottom” vertical modes and evaluated with observations from the Oregon continental slope. To better understand the observations, local tidal dynamics are modeled with a superposition of two idealized numerical simulations, one forced by local surface-tide velocities and the other by an obliquely incident internal tide generated at the Mendocino Escarpment 315 km southwest of the study site. The simulations reproduce many aspects of the observed internal tide and verify the modal-energy balances. Observed transfer of tidal energy into high-mode internal tides is quantitatively consistent with observed turbulent kinetic energy (TKE) dissipation. Locally generated and incident simulated internal tides are superposed with varying phase shifts to mimic the effects of the temporally varying mesoscale. Altering the phase of the incident internal tide alters (i) internal-tide energy flux, (ii) internal-tide generation, and (iii) energy conversion to high modes, suggesting that tidally driven TKE dissipation may vary between 0 and 500 watts per meter of coastline on 3–5-day time scales. Comparison of observed in situ internal-tide generation and satellite-derived estimates of surface-tide energy loss is inconclusive.

Wind directly forces inertial oscillations in the mixed layer. Where these currents hit the coast, the no-normal-flow boundary condition leads to vertical velocities that pump both the base of the mixed layer and the free surface, producing offshore-propagating near-inertial internal and surface waves, respectively. The internal waves directly transport wind work downward into the ocean’s stratified interior, where it may provide mechanical mixing. The surface waves propagate offshore where they can scatter over rough topography in a process analogous to internal-tide generation. Here, we estimate mixed layer currents from observed winds using a damped slab model. Then, we estimate the pressure, velocity, and energy flux associated with coastally generated near-inertial waves at a vertical coastline. These results are extended to coasts with arbitrary across-shore topography and examined using numerical simulations. At the New Jersey shelfbreak, comparisons between the slab model, numerical simulations, and moored observations are ambiguous. Extrapolation of the theoretical results suggests that (10%) of global wind work (i.e., 0.03 of 0.31 TW) is transferred to coastally generated barotropic near-inertial waves.

A complex superposition of locally forced and shoaling remotely generated semidiurnal internal tides occurs on the Oregon continental slope. Presented here are observations from a zonal line of five profiling moorings deployed across the continental slope from 500 to 3000 m, a 24-h expendable current profiler (XCP) survey, and five 15–48-h lowered ADCP (LADCP)/CTD stations. The 40-day moored deployment spans three spring and two neap tides, during which the proportions of the locally and remotely forced internal tides vary. Baroclinic signals are strong throughout spring and neap tides, with 4–5-day-long bursts of strong cross-slope baroclinic semidiurnal velocity and vertical displacement . Energy fluxes exhibit complex spatial and temporal patterns throughout both tidal periods. During spring tides, local barotropic forcing is strongest and energy flux over the slope is predominantly offshore (westward). During neap tides, shoaling remotely generated internal tides dominate and energy flux is predominantly onshore (eastward). Shoaling internal tides do not exhibit a strong spring–neap cycle and are also observed during the first spring tide, indicating that they originate from multiple sources. The bulk of the remotely generated internal tide is hypothesized to be generated from south of the array (e.g., Mendocino Escarpment), because energy fluxes at the deep mooring 100 km offshore are always directed northward. However, fluxes on the slope suggest that the northbound internal tide is turned onshore, most likely by reflection from large-scale bathymetry. This is verified with a simple three-dimensional model of mode-1 internal tides propagating obliquely onto a near-critical slope, whose output conforms fairly well to observations, in spite of its simplicity.

Spectral analyses of two 3.5-yr mooring records from the Timor Sea quantified the coherence of mode-0 (surface) and mode-1 (internal) tides with the astronomical tidal potential. The noncoherent tides had well-defined variance and were most accurately quantified for tidal species (as opposed to constituents) in long records (>6 months). On the continental slope (465 m), the semidiurnal mode-0 and mode-1 velocity and mode-1 pressure variance were 95%, 68%, and 56% coherent, respectively. On the continental shelf (145 m), the semidiurnal mode-0 and mode-1 velocity and mode-1 pressure variance were 98%, 34%, and 42% coherent, respectively. The response method produced time series of the semidiurnal coherent and noncoherent tides. The spectra and decorrelation time scales of the semidiurnal tidal amplitudes were similar to those of the barotropic mean flow and mode-1 eigenspeed (~4 days), suggesting local mesoscale variability shapes noncoherent tidal variability. Over long time scales (>30 days), mode-1 sea surface displacement amplitudes were positively correlated with mode-1 eigenspeed on the shelf. At both moorings, internal tides were likely modulated during both generation and propagation. Self-prediction using the response method enabled about 75% of semidiurnal mode-1 sea surface displacement to be predicted 2.5 days in advance. Improved prediction models will require realistic tide–topography coupling and background variability with both short and long time scales.