Collaborative Research: Internal waves impinging on near-critical slopes: multiscale numerical quantification of localized mixing and exchange with the interior

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The project will pursue a numerical investigation of boundary processes driven by internal waves and tides incident on a sloping bottom. In particular, the project will give a quantitative assessment of the hypothesis that nonlinear breakdown of internal waves at critical and near-critical slopes results in mixed fluid that then disperses along isopycnals to the interior, a problem of fundamental importance to diagnose the global ocean circulation. There is indirect support of this hypothesis through observations of intermediate nepheloid layers in the vicinity of near-critical slopes as well as direct evidence through laboratory experiments, albeit at low Reynolds number. Accurate estimates of local dissipation rates and turbulent transport coefficients at these ?hot spots? will also be provided by the simulations. There is mounting evidence through field observations that bottom boundary processes are important to the exchange of fluid between slopes and the interior, to energy pathways in the ocean, the suspension and settling of sediment, and to local biological productivity. It is thus necessary to improve our understanding and our ability to numerically predict the internal wave/boundary interaction problem and a multi-scale approach, with potentially transformative outcomes, will bridge the large internal wave scales to the bottom boundary layer (BBL).Realistic simulations of bottom mixing processes have not been possible so far because of the scale disparity between the incident wave field and the turbulence, the high Reynolds number of pre-existing boundary layers as well as those that form in the case of critical slope, and the high numerical dissipation used for stability in current ocean models. The scale-separation problem is handled here through a novel hierarchical use of analytical or numerical solutions for the large-scale problem coupled to a large eddy simulation (LES) of bottom mixing. To provide the large-scale field when analytical theories are not available, we will employ a new baroclinic model based on Adaptive Mesh Refinement (AMR). A realistic description of small-scale processes will be obtained here by employing LES with a sophisticated sub-grid model. This sub-grid model has a scale-similarity component to account for deviations from isotropic, inertial-range behavior, it is not unduly dissipative, it does not need tunable coefficients, and it has a near-wall component to account for the turbulence at the boundary layer roughness scale. The AMR and LES will be two-way coupled. The AMR (when needed) will drive the LES, while the latter will provide approximated boundary conditions for the former allowing communication of boundary mixing into the interior. The simulations will be analyzed for BBL properties, phasing of local mixing rates, lateral dispersal of BL mixed fluid, and characteristics of the nonlinearly scattered wave. Functional relationships to the properties of the incoming wave and to the slope angle will be extracted. Comparisons with laboratory and field data will be performed.Numerical large-scale models at the regional or global level are asked to provide increasingly precise evaluations of oceanic impact on climate change, depend on parameterizations for boundary fluxes. The AMR and LES simulations proposed here will allow a careful assessment of bottom turbulence dynamics which could then be used to develop an accurate representation of the bottom mixing component of large-scale models. Mixing along slopes affects several characteristics of the shelf-edge/slope area, which in turn control the exchange of nutrients and pollutants between the boundary and the open ocean. On a broader horizon, mixing at hot spots on shelf slopes is a critical ingredient in the energy balance of the internal wave field. Two PhD students will be trained across the fields of oceanography, engineering and computational science. Undergraduate students will be given the opportunity to participate in the research.