Program

    Although an accurate representation of ocean mixing processes into global circulation models is essential for accurate climate predictions, parameterization of mixing over rough bathymetry have plenty of room for improvement. For example, they do not take into account the fact that, as tide-topography interactions strengthen (k_HU₀/Ω >1), the generated internal waves transform from linear internal tides to quasi-steady internal lee waves (Mohri et al. 2010) where U₀ is the amplitude of the tidal flow dominating the background flow in the Garrett-Munk (GM) internal wave field, k_H is the horizontal wavenumber of the bottom topography, and Ω is the semidiurnal tidal frequency. 

    In this study, using a fixed value of the buoyancy frequency, we perform a series of eikonal calculations to examine the transfer of energy from upward propagating quasi-steady internal lee waves to dissipation through nonlinear interactions with the background GM internal waves in a vertical two-dimensional plane. It is shown that the vertical structure of the mixing hotspot becomes dominated by U₀ rather than k_H. As U₀ increases, the magnitude of the normalized energy dissipation rate at the ocean bottom decreases and its vertical decay scale increases. These calculated results can be interpreted in terms of the vertical group velocity, C_gz, and the life time, τ, of the upward propagating quasi-steady lee wave packet. For a fixed density stratification, as k_H increases while keeping U₀ constant, C_gz becomes larger but 𝜏 becomes smaller so that the vertical decay scale of the energy dissipation rate remains nearly constant, whereas C_gz becomes larger but 𝜏 remains unchanged as U₀ increases while keeping k_H constant so that the vertical decay scale of the energy dissipation rate rapidly increases. This means that the resulting mixing hotspot extends further upward as U₀ increases, independent of k_H. This is in contrast to the result of the previous study by Iwamae et al. (2009) and Iwamae and Hibiya (2012) who showed that the resulting mixing hotspot becomes more restricted to the ocean bottom as k_H increases, independent of U₀, although a trade-off relationship between the normalized energy dissipation rate at the ocean bottom and its vertical extent is found. A possible explanation for this difference is that C_gz and τ are both inversely proportional to k_H. 

    The results of this study should be reflected in the parameterization of mixing over rough bathymetry to improve the accuracy of ocean general circulation models.