An experimental study of critical layers

Abstract

Laboratory experiments have been made to investigate the development of internal gravity waves as they approach a critical layer where their phase speed is equal to that of the mean flow. The waves are produced in the accelerating flow of a stratified fluid in a long tilted tube in which the lower boundary has sinusoidal corrugations. As found in earlier experiments, the waves are not observed to propagate beyond the critical layer. Near the layer their amplitude increases, with the development of regions in which the fluid is gravitationally unstable. Kelvin-Helmholtz instability is not observed, perhaps because of viscous effects.A model is devised which describes the weakly nonlinear development of the waves. This is solved numerically. The results compare favourably with the experiments until gravitational instability is imminent. The numerical model is used to estimate both the second order Eulerian ‘jet’, which develops below the critical layer, and the Stokes drift. In the cases examined, the maximum drift is stronger than the jet and opposite in direction. The numerical model predicts the regions of wave breaking quite well.Internal gravity waves in the ocean may be modified by transient critical layers, for example those caused by vertically-propagating near-inertial oscillations.