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Abstract Coastal trapped waves (CTWs) transport energy along coastlines and drive coastal currents and upwelling. CTW modes are nonorthogonal when frequency is treated as the eigenvalue, preventing the separation of modal energy fluxes and quantification of longshore topographic scattering. Here, CTW modes are shown to be orthogonal with respect to energy flux (but not energy) when the longshore wavenumber is the eigenvalue. The modal evolution equation is a simple harmonic oscillator forced by longshore bathymetric variability, where downstream distance is treated like time. The energy equation includes an expression for modal topographic scattering. The eigenvalue problem is carefully discretized to produce numerically orthogonal modes, allowing CTW amplitudes, energy fluxes, and generation to be precisely quantified in numerical simulations. First, a spatially uniform K 1 longshore velocity is applied to a continental slope with a Gaussian bump in the coastline. Mode-1 CTW generation increases quadratically with the amplitude of the bump and is maximum when the bump’s length of coastline matches the natural wavelength of the CTW mode, as predicted by theory. Next, a realistic K 1 barotropic tide is applied to the Oregon coast. The forcing generates mode-1 and mode-2 CTWs with energy fluxes of 6 and 2 MW, respectively, which are much smaller than the 80 MW of M 2 internal-tide generation in this region. CTWs also produce 1-cm sea surface displacements along the coast, potentially complicating the interpretation of future satellite altimetry. Prospects and challenges for quantifying the global geography of CTWs are discussed. 

Abstract As part of a National Oceanographic Partnership Program (NOPP) project, seven teams—comprising investigators from universities, federal laboratories, and industry—are collaboratively investigating the generation, propagation, and dissipation of internal waves in the global ocean using complementary, state-of-the-art observations and model simulations. Internal waves, generated by the interaction of tides, winds, and mean flows, permeate the ocean and influence its physical state. Internal waves transport scalar and vector properties—both geographically and across scales—and contribute to irreversible mixing, modulate acoustic propagation, and complicate the identification of subinertial (e.g., geostrophic) flows in observations. For these reasons, accurately representing internal waves in global ocean forecast models is a high priority. The collaborations reported here are improving the understanding of the internal wave life cycle and enhancing model skill in simulating it. Three observational teams are collecting in situ data using 1) redeployable moored arrays that resolve internal waves from multiple directions, 2) global deployments of profiling floats that measure internal wave energy fluxes, shear, and mixing, and 3) high-resolution arrays that focus on bottom boundary layer processes. Four modeling teams are guiding the design and placement of these observation platforms and are using the collected observations to 1) improve internal wave representation and dissipation in ocean models, 2) conduct high-resolution process studies, and 3) implement data assimilation in idealized, regional, and global simulations. These efforts are further supported by high-resolution sea surface height measurements from the new Surface Water and Ocean Topography (SWOT) satellite, which provide context for in situ observations and improve ocean forecasting systems. Significance StatementA collaboration among scientists from U.S. universities, national laboratories, and industry is advancing our understanding and prediction of internal waves in the global ocean. These waves—characterized by vertical scales of tens to hundreds of meters and horizontal scales of tens to hundreds of kilometers—play a critical role in maritime commerce, naval operations, and ocean circulation. The team integrates novel observational approaches, including internal wave–resolving moored arrays, ship-of-opportunity float deployments, bottom boundary layer–distributed sensor networks, and satellite wide-swath altimetry, with cutting-edge global, regional, and process-model simulations. Together, these efforts are improving the representation of internal wave processes in ocean models and enhancing their predictive capabilities for operational forecasts. 

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 [Formula: see text](10%) of global wind work (i.e., 0.03 of 0.31 TW) is transferred to coastally generated barotropic near-inertial waves.