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Spectral evolution of bottom-forced internal waves

Recent observations and analysis suggest that rough abyssal topography serves as a generation site for energetic internal waves. The elevated turbulence that these waves produce may be an important part of global circulation and energy budgets. We have conducted a series of idealized numerical experiments to investigate internal wave evolution and interaction above rough topography. The non-hydrostatic equations of motion are solved in a horizontally periodic, domain with free-slip top and bottom boundary conditions, allowing nonlinear interactions between about 105 wave modes. We do not explicitly consider the wave generation problem, but instead force each simulation with a narrowband, upwardly propagating internal tide as a (near) bottom boundary condition. Three simulations are run with varying amplitude at a low-latitude (26 ◦ S) chosen to match the Brazil Basin mixing experiment. For comparison, three simulations were also run at at mid-latitude (45 ◦ S). In all cases nonlinear interactions quickly transfer energy to a wide range of scales and frequencies. Once a quasi-steady state is achieved, energy spectra are characterized by high-frequency slopes with close spectral slopes close to -2, in qualitative agreement with numerous observations and models. In contrast, vertical wavenumber spectra retain more of a narrowband signature, with deviations in shape that respond sensitively to changes in forcing amplitude. Two-dimensional spectra are non-separable in vertical wavenumber and frequency, with a band of energy at lowwavenumbers extending through all frequencies. The numerical predictions of turbulent dissipation appear to be realistically patchy in space and time with a strongly decreasing trend with height in all simulations. All simulations yield an approximately quadratic relationship between the average shear variance and the volume integrated dissipation rate. There are two major distinctions between lowand mid-latitude results. First, at low-latitude, nonlinear interactions transfer energy from tidal to near-inertial waves, while at mid-latitude energy remains concentrated near the forcing frequency (M2) and wavenumber. At low-latitude, the frequency shift occurs within a few days of the initiation of forcing. Second, the average mid-latitude dissipation rate is larger than that at low-latitude for comparable wavefield energy, especially near the forcing region, qualitatively consistent with observations and theoretical predictions. We hypothesize that the dramatic difference in the rate of energy transfer out of the tidal band between the lowand mid-latitude experiments is loosely related to Parametric Subharmonic Instability (PSI) an idealized type of wave-wave interaction possible only at low latitudes.