Benjamin King

Experimental study of internal gravity waves generated by supercritical topography

Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of D. G. Hurley and G. Keady [J. Fluid Mech. 351, 119 (1997)]. The width of the wave beams is determined by competition between forcing and viscous smoothing, and hydrodynamic screening of the steep part of the topography extends the cylinder’s horizontal length scale. Beyond the weak forcing regime, harmonic waves of frequency nΩ (with integer n>1 and nΩ<N, where N is the buoyancy frequency) are generated mainly by nonlinear interaction involving the overlapping fundamental waves. For moderate forcing we find that the intensity of the fundamental and second harmonic waves scales linearly and quadratically with A, respectively.Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of ...

Tidal flow over three-dimensional topography in a stratified fluid

Our laboratory experiments and numerical simulations of stratified tidal flow past model topography (a half sphere on a horizontal plane) reveal several three-dimensional flow features, including an unexpected flow perpendicular to the forcing plane (the vertical plane through the center of the sphere, in the direction of the oscillating tide). This perpendicular flow has a time-independent component and a component oscillating at twice the tidal frequency. Our results show that the time-independent part of the perpendicular flow forms a large-scale horizontal circulation, which could enhance material transport and mixing near bottom topography in the oceans. In addition, for small forcing amplitude we find that the azimuthal dependence of the internal wave field is described by the functional form cos ϕ, as predicted by linear inviscid theory. At higher forcing amplitude, the internal wave energy is more concentrated in the forcing direction. Finally, we observe a wave intensity asymmetry in the polar di...