On the generation and evolution of internal gravity waves

Abstract

In order to study the tidal generation and evolution of internal waves, both experimentally and theoretically, a two-dimensional two-layer model has been developed. The laboratory model consists of two immiscible fluid layers in a long wave tank, where time-dependent flow can be created by towing a suitably shaped obstacle with a sinusoidal motion. The effects of changing the Froude number and the ratio of the depths of the two fluid layers on the shape of the interface are studied. The first theoretical model considers the motion to be quasi-steady, allowing only a balance between buoyancy and inertial forces, and is in reasonable agreement with the experimental results for very slow motions and the initial phase of the tidal cycle only. A more complete numerical solution is based on the vortex-point method in which the interface is modelled by a set of discrete vortices, while the rigid boundaries, which include the obstacle, are modelled by a source distribution. The resulting governing equations are expressed in Lagrangian form, and the baroclinic generation of vorticity is related to the generation of source density, through two simultaneous integrodifferential equations. For small Froude numbers, the experimental and numerical results are in good quantitative agreement. At large Froude numbers, the numerical solution, which does not consider mixing between the two layers nor boundary-layer separation from the obstacle, gives a slight difference in the position of the maximum interface displacement from that found in the experiment.