Barotropic tidal oscillations over seafloor topography generate baroclinic tides which may be damped in turn via nonlinear triad interactions with internal gravity waves, fuelling the ambient wave field. We derive the kinetic equations for this tidal damping and the energy transfer to the ambient wave field and compute damping times and energy transfer rates for the M2 tide and a Garrett-Munk-like ambient wave field. We show that parametric subharmonic instability (PSI) interactions are important, where the tide interacts resonantly with two background waves, each of half the tidal frequency. PSI is restricted to the latitude belt 28.8° N/S and yields under typical conditions damping times of about 20 days for tides with low vertical wavenumber. Damping times decrease with equivalent mode number j roughly as 1/ j2. Outside the critical latitudes PSI is not possible and damping times are one to two orders of magnitude larger. The energy transfer to the ambient wave field is concentrated at half the tidal frequency ω at all latitudes within the critical latitude belt. Outside, the transfer is much smaller and peaks at ω + f and N. An estimation of the tidal spectral transfer on the global scale is hampered by insufficient knowledge of the baroclinic energy distribution over the vertical modes. Using results from a numerical circulation model with tidal forcing, we find an energy transfer from the tide to the ambient wave field of typically 0.3 TW, about half of what is currently proposed for the conversion of barotropic to baroclinic energy.
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