There is uncertainty about nonlinear internal wave interaction rates, particularly in the near-inertial part of the spectrum. This project is directed at understanding the role of parametric sub-harmonic instability (PSI) in transferring energy from large-scale, coherent internal gravity waves generated by tides and wind to the near-inertial peak of the oceanic internal wave spectrum. The hypothesis is that PSI is a rapid and robust mechanism for driving fast, near-inertial oscillations with small vertical scale. This transfer of energy from 2 f0 to the neighborhood of f0 requires the right circumstances (e.g., PSI is most effective at resonant latitudes). If the hypothesis is true, then PSI is a prelude to ocean mixing and the geographic and environmental factors modulating PSI also play an important role in controlling the spatial distribution of mixing and vertical fluxes in the ocean.
The assessment of the hypothesis above requires new, quantitative estimates of the rate at which PSI transfers energy from mode one internal gravity waves into the near-inertial peak. To be realistic, these estimates must take account of the-effect and the vertical mode one structure of internal tidal wave trains. Thus the goal fo the project is to obtain analytic estimates of the rate at which PSI drains energy from a low vertical mode wave train in a realistically stratified ocean. Numerical simulations will provide a useful check on these results and enable exploration the nonlinear development of the instability.
Validation of the hypothesis also requires an assessment of the role of geostrophic eddies in catalyzing PSI and in spatially organizing near-inertial waves. Because of their spatial and temporal coherence, geostrophic eddies create important inhomogeneities in the oceanic environment through which internal gravity waves propagate. Specifically, the effective inertial frequency differs from the actual inertial frequency by half of the relative vorticity of the the geostrophically balanced flow. This frequency shift has a potent effect on the near-inertial peak and may broaden the 2 f0-resonance required for PSI. These issues involving the near-inertial spectral peak, geostrophic eddies and PSI can be addressed under a unified theoretical framework and the core of the proposal is to develop, test and apply this theory.
Broader impacts: Ocean mixing rates cannot be characterized by a single universal diffusivity and thus it is essential to understand how spatial, temporal and environmental factors affect the supply of energy to the near-inertial peak. Better representation of eddy fluxes are required so that oceanographers can reliably model or diagnose the ocean's role in climate, the ocean carbon cycle, the nutrient supply to the euphotoic zone and the intentional deep-water disposal of carbon and other industrial waste products. Understanding the role of tides, internal gravity waves and topographic interactions in establishing these eddy fluxes is the target of this project. In addition, a graduate student will be trained in both theory and numerical modeling in physical oceanography.
