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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 K1 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 K1 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 M2 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 FROM AUTHOR]

Observations of breaking internal tides on the Oregon continental slope during a 40-day deployment of 5 moorings along 43°12′N are presented. Remotely generated internal tides shoal onto the slope, steepen, break, and form turbulent bores that propagate upslope independently of the internal tide. A high-resolution snapshot of a single bore is captured from lowered acoustic Doppler current profilers (LADCP)/CTD profiles in a 25-h time series at 1200 m. The bore is cold, salty, over 100 m tall, and has a turbulent head where instantaneous dissipation rates are enhanced ( ε > 10−6 W kg−1) and sediment is resuspended. At the two deepest slope moorings (1452 and 1780 m), similar borelike phenomena are observed in near-bottom high-resolution temperature time series. Mean dissipation rates and diapycnal diffusivities increase by a factor of 2 when bores are present ( W kg−1 and m s−1) and observed internal tides are energetic enough to drive these enhanced dissipation rates. Globally, the authors estimate an average of 1.3 kW m−1 of internal tide energy flux is directed onto continental slopes. On the Oregon slope, internal tide fluxes are smaller, suggesting that it is a relatively weak internal tide sink. Mixing associated with the breaking of internal tides is therefore likely to be larger on other continental slopes. [ABSTRACT FROM AUTHOR]