Tidally generated internal waves at long-wavelength bottom topography that are radiated into the interior to subsequently breakdown into small scales may be a significant contributor to diapycnal mixing. The interaction of the tide with smaller-scale topography is also relevant to near-field mixing as exemplified by recent data from moored instruments taken as part of the Hawaii Ocean Mixing Experiment (HOME) near-field survey that indicate increased levels of dissipation and variability in a rather thick bottom region, O(250)m, depending on the tidal phase. The mixing characteristics of a stratified current oscillating on a rough slope with M2 tidal period are poorly understood. High-accuracy, numerical simulations with a non-hydrostatic model will be conducted to understand the relevant processes underlying the observed behavior of the bottom boundary layer. The modulation by a M2 tide of a current in the deep ocean over rough topography is considered. In the model problem, a shallow slope represents the large-scale topography while Gaussian roughness elements of specified height and pitch represent the small-scale topography. The value of the Brunt-Vaisala frequency, near the bottom changes in response to the tidal modulation, and the interaction of the time-dependent stratification with the current as it accelerates, decelerates or potentially separates over the small-scale roughness is of interest. The physics relevant to this problem is fundamentally different from the internal wave generation problem and, although important, has been much less studied than the latter. The Large Eddy Simulation will be performed with advanced numerical methods for the unsteady, three-dimensional, Navier-Stokes equations in primitive form without any hydrostatic assumption. The subgrid model to be used is a dynamic mixed model with wall-layer modeling. A generalized coordinate formulation allows the grid to track the bottom topography, helpful for maintaining accuracy. Parameters relevant to the HOME situation will be chosen in conjunction with HOME PI's. The scaling of the effective boundary layer thickness and profiles of the Vaisala frequency, buoyancy flux, fluctuation intensities and eddy diffusivities as a function of important nondimensional parameters will be obtained.
Broader Impacts: The results of the proposed research will help understand the link between the mixing observed in an unexpectedly thick region near the bottom and the M2 tidal modulation and thus impact physical oceanography. Given our lack of knowledge about mixing in an oscillating boundary layer over rough topography in a stratified, rotating medium, it is expected that this study will result in a substantive contribution to geophysical fluid dynamics as well.
