Internal wave generation by oscillation of a sphere, with application to internal tides

Abstract

A joint theoretical and experimental study is performed on the generation of internal gravity waves by an oscillating sphere, as a paradigm of the generation of internal tides by barotropic tidal flow over three-dimensional supercritical topography. The theory is linear and three-dimensional, applies both near and far from the sphere, and takes into account viscosity and the unsteadiness arising from the interference with transients generated at the start-up. The waves propagate in conical beams, evolving with distance from a bimodal to unimodal wave profile. In the near field, the profile is asymmetric with its major peak towards the axis of the cones. The experiments involve horizontal oscillations and develop a cross-correlation technique for the measurement of the deformation of fluorescent dye planes to sub-pixel accuracy. At an oscillation amplitude of one fifth of the radius of the sphere, the waves are linear and the agreement between experiment and theory is excellent. As the amplitude increases to half the radius, nonlinear effects cause the wave amplitude to saturate at a value that is 20% lower than its linear estimate. Application of the theory to the conversion rate of barotropic tidal energy into internal tides confirms the expected scaling for flat topography, and shows its transformation for hemispherical topography. In the ocean, viscous and unsteady effects have an essentially local role, in keeping the wave amplitude finite at the edges of the beams, and otherwise dissipate energy on such large distances that they hardly induce any decay.