The role of internal tides in mixing the deep ocean

Internal wave theory is used to examine the generation, radiation, and energy dissipation of internal tides in the deep ocean. Estimates of vertical energy flux based on a previously developed model are adjusted to account for the influence of finite depth, varying stratification, and two-dimensional topography. Specific estimates of energy flux are made for midocean ridge topography. Weakly nonlinear theory is applied to the wave generation at idealized topography to examine finite amplitude corrections to the linear theory. Most internal tide energy is generated at low modes associated with spatial scales from roughly 20 to 100 km. The Richardson number of the radiated internal tide typically exceeds unity for these motions, and so direct shear instability of the generated waves is not the dominant energy transfer mechanism. It also seems that wave-wave interactions are ineffective at transferring energy from the large wavelengths that dominate the energy flux. Instead, it appears that most of the internal tide energy is radiated over O(1000 km) distances. A small fraction of energy flux, less than 30%, is generated at smaller spatial scales, and this energy flux may dissipate locally. Estimates along the Mid-Atlantic Ridge in the South Atlantic suggest that the vertical energy flux of M-2 internal tides is 3-5 mW m(-2), with 1-2 mW m(-2) likely contributing to local mixing. Along the East Pacific Rise, bathymetry is more smooth and tides are weaker, and estimates suggest internal tide energy flux is negligible. Radiated low modes are likely influenced by topographic scattering, though general topography scatters less than 10% of the low-mode energy to higher wavenumbers. Thus, low-mode internal tides may contribute to mixing at locations far away from their generation sites.