A parameterization of local and remote tidal mixing

Abstract

Vertical mixing is often regarded as the Achilles' heel of ocean models. In particular, few models include a comprehensive and energy-constrained parameterization of mixing by internal ocean tides. Here, we present an energy-conserving mixing scheme which accounts for the local breaking of high-mode internal tides and the distant dissipation of low-mode internal tides. The scheme relies on four static two-dimensional maps of internal tide dissipation, constructed using mode-by-mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three-dimensional map of dissipation which compares well with available microstructure observations and with upper-ocean finestructure mixing estimates. This relative agreement, both in magnitude and spatial structure across ocean basins, suggests that internal tides underpin most of observed dissipation in the ocean interior at the global scale. The proposed parameterization is therefore expected to improve understanding, mapping, and modeling of ocean mixing.Plain Language Summary When tidal ocean currents flow over bumpy seafloor, they generate internal tidal waves. Internal waves are the subsurface analog of surface waves that break on beaches. Like surface waves, internal tidal waves often become unstable and break into turbulence. This turbulence is a primary cause of mixing between stacked ocean layers-a key process regulating ocean currents and biology and a key ingredient of computer models of the global ocean. In this article, a three-dimensional global map of mixing induced by internal tidal waves is presented. This map incorporates a large variety of energy pathways from the generation of tidal waves to turbulence, accounting for the conservation of energy. The map is compared to available observations of turbulence across the globe and found to reproduce with good fidelity the main patterns identified in observations. This relatively good agreement suggests that internal tidal waves are the main source of turbulence in the subsurface ocean and implies that the map may serve a range of applications. In particular, the three-dimensional map provides an efficient and realistic means to represent mixing by internal tidal waves in global ocean models.

Empirical Lagrangian parametrization for wind-driven mixing of buoyant particles at the ocean surface

“…In addition, the influence of wind forcing on turbulence is generally assumed to be limited to the surface mixed layer (Chamecki et al, 2019), while with the SWB profile wind-generated turbulence can extend below the MLD. To represent sub-MLD mixing, either a constant K z value or other K z profiles could be used, such as the K z estimates for internal tide mixing as proposed by de Lavergne et al (2020).…”

Radiation Path of Diurnal Internal Tides in the Northwestern Pacific Controlled by Refraction and Interference

“…Figures 17c and 17d show that the energy dissipation along the LS and THP beam lines exhibits different magnitudes between July and January. Although further study combining in situ observations with refined numerical simulations is required, this phenomenon is presumably caused by seasonal differences in eddy scattering effects (Dunphy & Lamb, 2014), density stratification structures (de Lavergne et al., 2020; Melet et al., 2013) and subtidal current shear (Kerry et al., 2014a).…”

The role of mixing in the large-scale ocean circulation

“…, principally internal tides(Ledwell et al 2000, de Lavergne et al 2020. Using a realistic map of mixing fueled by internal tides (de Lavergne et al 2020), we estimate that tidal mixing converts about 15 Sv of 28.11-28.2 kg m −3 waters into lighter 28.05-28.11 kg m −3 waters (Fig.8b).…”

“…Away from boundaries, moderate turbulence levels are largely sustained by the breaking of internal waves generated by tides (Fig. 3a,b; Kunze et al 2006, Waterhouse et al 2014, de Lavergne et al 2020. Three-dimensional turbulence mixes tracers and momentum alike, although the isotropic diffusivities of momentum and tracers can differ (Gaspar et al 1990).…”