A Heuristic Description of Internal Wave Dynamics

Abstract

The oceanic internal wave spectrum has long been interpreted as being shaped by nonlinear processes. The empirical Garrett and Munk synthesis of oceanic observations is E(m, ?) ? Nm?2??2 at high wavenumber and frequency. Results of both approximate analytic and numerical estimates of weak nonlinear interactions under the resonant interaction approximation have previously been interpreted as implying the dominance of scale-separated interactions and that the Garrett and Munk spectrum is stationary with respect to the nonlinear interactions. However, dimensional analysis cobbled together with several basic observational constraints requires a stationary spectrum of E(m, ?) ? Nm?2??3/2 at high vertical wavenumber and frequency. Given this stationary spectrum, dimensional analysis and extant data are used to infer a flux representation for the spectral transports. The resulting semiempirical flux laws can be described as a relaxation to the stationary power laws. The stationary spectrum is consistent with energy sources at low frequencies and dissipation at higher frequencies and vertical wavenumber. The analysis is then extended to include vertically asymmetric wave fields. Vertical wavenumber spectra of horizontal velocity that exhibit a difference between rotary (clockwise and counterclockwise phase rotation of the velocity vector with depth) spectra at large wavelengths tend to be symmetric at smaller scales. This pattern is hypothesized to be a result of nonlinearity within the wave field. In particular, vertical symmetry is linked here to the issue of momentum conservation. A backscattering process is invoked to achieve momentum conservation. This representation of nonlinearity is used in a numerical scheme to assess the spatial evolution of a bottom-generated wave field. The predicted patterns of relaxation and vertical symmetry are in reasonable agreement with finescale observations above rough bathymetry in the Brazil Basin.