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.
Song, Charles; Hwang, Jack.
The Generation of Internal Waves in Stratified Fluids.
St. Anthony Falls Hydraulic Laboratory.
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