The Role of Vertical Divergence in Internal Wave/Wave Interactions

Smallscale internal waves are numerically ray-traced through random 3-D Garrett and Munk (GM) internal wave backgrounds. Past ray-tracing investigations have considered only interactions with background vertical shear Vz = (Uz, Vz). Our numerical simulations indicate a non-negligible role for vertical divergence Wz. The spectral transfer of internalwave energy toward high vertical wavenumber kz and turbulence production ε are 2–4 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 scaleseparation Kz < 0.5kz and horizontal scale-separation KH < kh for background frequencies Ω > 11f. Imposing WKB horizontal scale-separation at all background frequencies caused 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.