Dynamical Analysis of the Enhanced Turbulent Mixing Over a Rough Ocean Bottom

Toshiyuki Hibiya1, Robin Robertson2 and Tomoaki Takagi1, (1)The University of Tokyo, Department of Earth and Planetary Science, Graduate School of Science, Tokyo, Japan, (2)The University of New South Wales, School of Physical, Environmental, and Mathematical Sciences, Canberra, Australia
Abstract:
Although an accurate representation of ocean mixing processes in global circulation models is essential, parameterization of mixing over rough bathymetry remains obscure. We perform here a series of vertical two-dimensional numerical experiments to see how upward propagating internal waves generated by the tide-topography interaction give up their energy to dissipation by nonlinear interaction with the background Garrett-Munk-like internal waves.

The internal waves generated by the tide-topography interaction are classified in terms of the parameters kU0 /ω and N/ω with U0 the tidal flow amplitude, k the wavenumber of bottom bathymetry, N the buoyancy frequency and ω the semidiurnal tidal frequency. When kU0 /ω ≪ 1, linear internal tides are generated and propagate upward with the decay scale controlled by bottom roughness rather than by the tidal flow amplitude. When kU0 /ω ≫ 1, on the other hand, generated internal waves become more like quasi-steady lee waves propagating upward with the decay scale controlled by the tidal flow amplitude rather than by bottom roughness.

To interpret these numerical results, we also perform eikonal calculations for a wide range of physical parameters. We confirm that, for a fixed value of N, the vertical group velocity Cgz is inversely proportional to k for linear internal tides but proportional to kU02 for quasi-steady lee waves. Since the resonant interaction time τ is inversely proportional to k for both cases, the resulting mixing hotspot becomes more restricted to the ocean bottom as bottom roughness increases for kU0 /ω ≪ 1 without depending on the tidal flow amplitude, but it extends upward as the tidal flow amplitude increases for kU0 /ω ≫ 1 without depending on bottom roughness. In both cases, we can find the trade-off relationship between the energy dissipation rate at the ocean bottom and its vertical extent.

The results of this study are summarized in the attached figure. The accuracy of global circulation models can be improved by reflecting these results in the parameterization of mixing over rough bathymetry.

Back to: Deep and Abyssal Ocean Mixing: From Small-Scale Turbulence to the Large-Scale MOC I