Internal Wave–Wave Interactions. Part II: Spectral Energy Transfer and Turbulence Production

Abstract

The spectral transfer of internal wave energy toward high vertical wavenumber kz and turbulence production ε is examined by ray tracing small-scale test waves in a canonical Garrett and Munk background wave field. Unlike previous ray-tracing studies, interactions with internal-wave vertical divergence Wz as well as vertical shear Vz are allowed. The resulting spectral energy transfer rates are 2 to 4 times shear-only predictions depending on the degree of vertical and horizontal scale separation imposed. An upper limit is obtained by imposing vertical scale separation Kz < kz and no restriction on horizontal wavenumber or frequency. This violates the WKB approximation in the horizontal and time. A lower limit is obtained by imposing stricter vertical scale separation Kz < 0.5kz and horizontal scale separation KH < kh for background frequencies Ω > 11f. Imposing WKB horizontal scale separation at all background frequencies causes some test waves to get stuck at low horizontal wavenumber and low frequency. This is not realistic. The shear and strain lower limit produces turbulence production rates close to the upper limit of shear-only calculations and therefore consistent with observations.