Internal wave and boundary current generation by tidal flow over topography

Abstract

The relationship between boundary currents generated by tidal flow over topography and the radiated internal wave power is examined in two-dimensional numerical simulations of a uniformly stratified fluid. The radiated power PIW and kinetic energy density of the boundary currents are computed as a function of the internal wave slope SIW and the criticality parameter ε (ratio of the maximum topographic slope to SIW). Both SIW and ε are varied two orders of magnitude about unity by changing the tidal frequency, stratification, or topographic shape and slope. We consider cases where the hydrostatic approximation is valid (SIW ≪ 1), as well as test theoretical predictions for models of the deep ocean where the beam slope diverges and the hydrostatic approximation fails. We confirm that resonant boundary currents characterized by large kinetic energy densities form over critical topography (ε = 1). However, we find that this resonance phenomenon does not extend to the power radiated by internal waves that propagate away from the topography. Further, by directly comparing the kinetic energy density to the energy flux of the generated internal waves, we find that the more easily measured kinetic energy density cannot be used as a proxy to characterize the conversion of tidal energy to radiated internal wave power. Whether the hydrostatic approximation is valid or fails, our measurements of the radiated power can be described as PIW = Ptidef (ε, shape)/SIW, where Ptide is the effective tidal power that interacts with the topography, and π/8 < f (ε, shape) < π/4 is bounded below by the theoretical prediction of Bell [“Topographically generated internal waves in the open ocean,” J. Geophys. Res. 80, 320–327 (1975)] for ε → 0 and above by Llewellyn Smith and Young [“Tidal conversion at a very steep ridge,” J. Fluid Mech. 495, 175–191 (2003)] for ε → ∞.