The Generation of Internal Waves in Stratified Fluids

Abstract

Internal waves in exponentially stratified fluids confined between two parallel boundaries have been studied analytically and experimentally with both a fixed and a free upper surfaoe. In the analytical model, waves were generated by vortex-like or sourcelike oscillatory disturbances. A modified image method was developed according to the principle of superposition using Hurley's elementary solutions for unbounded fluid. A basic image system which satisfies the wall boundary condition and is free of singularities in the flow field was found for every elementary vortex or source located anywhere in the field. The internal wave associated with this image system is intimately related to the characteristic mesh of the system. Only the first mode of the progressive internal wave is possible when the elementary vortex or source is located on the centerline of the channel. It appears that eccentrically located disturbances are required to generate higher mode internal waves, although numerical analysis has not been carried out for this case. An experiment was carried out in a channel filled with salt water of exponential density stratification. A rigid flat plate wave generator and a flexible rubber diaphragm wave generator located at mid-depth, both oscillating in a vertical direction, were used. Excellent agreement was obtained between the predicted and the measured wave length. The predicted wave shape and the measured wave shape were also in good agreement. Less complete agreement was obtained for the case of wave amplitude, however.