Eikonal Simulations for the Energy Transfer in the Deep Ocean Internal Wave Field near Mixing Hotspots

In the proximity of mixing hotspots, the observed internal wave spectra are usually distorted from the Garrett-Munk (GM) spectrum and are characterized by the high energy level E as well as the shear/strain ratio R_ω quite different from the corresponding value for the GM spectrum (R_ω = 3). Accurate parameterization of the energy transfer toward dissipation scales that takes into account the effects of E and R_ω is therefore indispensable to quantify the deep ocean mixing.

In this study, a series of eikonal simulations are carried out to examine energy transfer within such distorted internal wave spectra. The obtained results are used to assess the recently proposed parameterization for energy dissipation in the distorted internal wave field near mixing hotspots (Ijichi and Hibiya, 2015). In particular, several factors neglected by these authors in formulating the parameterization such as the background vertical divergence and the WKB horizontal scale-separation between small-scale test waves and the background waves are all taken into account throughout the eikonal simulations.

It is shown that the calculated energy transfer rate ε is fairly consistent with the scaling ε ~ E²N²f with N the local buoyancy frequency and f the local inertial frequency. Furthermore, the calculated results exhibit strong R_ω dependence quite similar to that predicted from the parameterization by Ijichi and Hibiya (2015), suggesting the validity of their formulation.