Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes

Abstract

In order to examine how the energy supplied by M2 internal tides cascades through the local internal wave spectrum down to dissipation scales, two sets of numerical experiments are carried out where the Garrett-Munk-like quasi-stationary internal wave spectra at 49°N (experiment I) and 28°N (experiment II), respectively, are first reproduced and then perturbed instantaneously in the form of an energy spike at the lowest vertical wave number and M2 tidal frequency. These experiments attempt to simulate the nonlinear energy transfer within the quasi-stationary internal wave fields near the Aleutian Ridge and the Hawaiian Ridge, respectively, both of which are generation of large-amplitude M2 internal tides. In experiment I, the energy spike stays at the lowest wave number, where it is embedded and the spectrum remains quasi-stationary after the energy spike is injected. In experiment II, in contrast, the energy level at high horizontal and vertical wave numbers rapidly increases after the injection of the energy spike, exhibiting strong correlation with the enhancement of high vertical wave number, near-inertial current shear. This implies that as the high vertical wave number, near-inertial current shear is intensified, high horizontal wave number internal waves are efficiently Doppler shifted so that the vertical wave number rapidly increases and enhanced turbulent dissipation takes place. The elevated spectral density in the high vertical wave number, near-inertial frequency band, which plays the key role in cascading energy to dissipation scales, is thought to be caused by parametric subharmonic instability. In experiment I, in contrast, the M2 tidal frequency is 1.2 times the inertial frequency at 49°N so that M2 internal tide is free from parametric subharmonic instability. Accordingly, even though significant M2 internal tidal energy may be generated, it is not available to support local deep water mixing.