Experiments on solitary internal Kelvin waves

Abstract

Elementary calculations indicate that the effect of the Earth's rotation is likely to be important in the dynamics of most internal waves in oceans, lakes and the atmosphere. Here we present measurements of the structure and properties of one class of such waves, namely solitary internal Kelvin waves, in which the Coriolis force generated by wave motion in a stratified fluid is opposed by a pressure gradient and hence change in wave amplitude along its crest. We confirm that the wave speed is independent of the rate at which the system rotates and depends only on the stratification and maximum wave amplitude. However, rotation is shown to have a large effect on both the rate at which the amplitude varies with time and the cross-stream’ structure of the wave. In accordance with well-established theory, the amplitude transverse to the direction of propagation varies exponentially. This results in a decreasing wave speed with increasing distance from the wall, which in turn requires the wave front be curved backwards in order for the wave as a whole to propagate at a speed given by its maximum amplitude. Such a front curvature is not contained within the available theories. The rapid decay of wave amplitude is found to be due to the generation of inertial waves in the homogeneous fluid above and below the internal wave, and a reasonably successful scaling of this effect has been found. We also discuss the adjustment of the waves to geostropic balance and comment on applications of our results to natural systems.