Energetics and Mixing of Stratified, Rotating Flow over Abyssal Hills

One of the proposed mechanisms for energy loss in the ocean is through dissipation of internal waves, in particular above rough topography where internal lee waves are generated. Rates of dissipation and diapycnal mixing are often estimated using linear internal wave generation theory and a constant value for mixing efficiency. However, previous oceanographic measurements found that nonlinear dynamics may be important close to topography. To investigate the role of nonlinear interactions, we conduct idealized 3D direct numerical simulations (DNS) of steady flow over 1D topography and vary the topographic height, which correlates to the degree of flow nonlinearity. We analyze the spatial distribution of energy transfer rates between internal waves and the nongeostrophic portion of the time-mean flow, and of dissipation and diapycnal mixing rates. In our simulations with taller, more nonlinear topographies, energy transfer rates are similar to previously unexplained oceanographic observations near topography: internal waves gain energy from time-mean flow through horizontal straining and lose energy through vertical shearing. In the tall topography simulations, buoyancy fluxes also play a significant role, consistent with observations but contrary to linear wave theory, suggesting that quasigeostrophy-based approximations and linear theory may not hold in some regions above rough topography. Both dissipation and mixing rates increase with topographic height, but their vertical distributions differ between topographic regimes. As such, the vertical profile of mixing efficiency is different for linear and nonlinear topographic regimes, which may need to be incorporated into parameterizations of small-scale processes in models and estimates of ocean energy loss.