Internal wave excitation by a vertically oscillating sphere

Abstract

The properties of waves generated by a vertically oscillating sphere in a uniformly stratified fluid are examined both theoretically and experimentally. Existing predictions for the wave amplitude and phase structure are modified to account for the effects of viscous attenuation. As with waves generated by an oscillating cylinder, the main effect of attenuation is to broaden the two peaks of the amplitude envelope on either flank of the wave beam so that far from the sphere the wave beam exhibits a single peak with a maximum along the centreline. The transition distance from bimodal to unimodal wave beam structure is shown to occur closer to the source than the corresponding distance calculated for the oscillating circular cylinder. For laboratory experiments, a recently developed ‘synthetic schlieren’ method is adapted so that quantitative measurements may be made of an axisymmetric wave field. This non-intrusive technique allows us to evaluate the amplitude of the waves everywhere in space and time. Experiments are performed to examine the amplitude of waves generated by small and large spheres oscillating with a range of amplitudes and frequencies. The wave amplitude is found to scale linearly with the oscillation amplitude $A$ for $A/a$ as large as 0.27, where $a$ is the radius of the sphere. Generally good agreement between theory and experiment is found for the small sphere experiments. However, the theory overpredicts both the amplitude and the bimodal-to-unimodal transition distance for waves generated by the large sphere.