0 50 50 50 v 1 1 9 M ay 2 00 5 Scale Invariant Spectra of the Oceanic Internal Wave Field

We present a theory predicting the high-frequency-high-wavenumber part of the spectral energy density of internal waves in the ocean. The theory is based on the wave turbulence formalism applied to a natural Hamiltonian description for the internal wave field. We show that stationary energy spectra form a family of statistically steady state scale invariant solutions. Remarkably, the high-frequency-high-wave number limit of the celebrated Garrett and Munk spectrum is a member of this family. We re-analyze many major oceanographic internal waves observational programs of the last 4 decades in order to characterize variability in the deep ocean internal wavefield. Data from long term current meter deployments typically reveal an annual cycle in high frequency energy, as noted previously, that covers the factor of 2-3 variability usually ascribed to the background wavefield. Overlain upon the temporal variability is a more subtle geographic pattern. Departures from the high frequency and high vertical wavenumber power laws of the Garret and Munk spectrum are seen to co-vary: whiter frequency spectra are partnered with redder vertical wavenumber spectra. Other signatures regarding separability of the 2-D vertical wavenumber frequency spectrum, departure from power law behavior and patterns related to spectral amplitude are also discussed. The family of solutions predicted by wave turbulence theory is consistent with this pattern of covariable power laws. We demonstrate that small, scale dependent perturbations to an otherwise scale invariant system provide a selection mechanism which picks the particular member of the family to be realized in each particular oceanographic setting. For oceanic waves, the most significant non scale invariant perturbations are the Coriolis effect, eddies and the ocean tides. The former, it turns out, selects the GM spectrum, while the latter may account for the variability in the observational set. Finally, we review previous theoretical work based upon a Lagrangian description of internal waves. We demonstrate that these previous calculations greatly overestimate the role of scale separated interactions.