Interaction of Water Waves with a Density-Stratified Fluid in a Rectangular Trench

Citation

Ting, Francis Chi Kin (1989) Interaction of Water Waves with a Density-Stratified Fluid in a Rectangular Trench. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8bgx-4e53. https://resolver.caltech.edu/CaltechETD:etd-02152007-151955

Abstract

The interaction of normally incident time-periodic water waves with a density-stratified fluid in a rectangular trench is studied experimentally and theoretically; the fluid outside the trench is homogeneous.

This investigation has focused on the excitation of internal waves in the trench by surface waves, and the effects of the internal oscillations on the waves on the free surface. The study shows that, when the frequency of the incoming surface waves corresponds to the natural frequency of oscillation of the internal waves in the trench, the amplitude of the internal waves becomes large compared to the amplitude of the surface waves. The effects of the internal waves on the surface waves were very small in the experiments.

A two-layer model and a three-layer model are developed and applied to a particular constant-depth channel and trench configuration used in the experiments. The two-layer model is also applied to a rectangular trench in an infinite region. These models treat steady-state wave motions of infinitesimal amplitude for all ranges of fluid depth relative to the wavelength of the surface waves, and include a vigorous treatment of the effects of energy dissipation in the laminar boundary layers adjacent to the solid surfaces and at the density interface. In the two-layer model the stratified fluid in the trench is represented by two homogeneous fluids of different densities; in the three-layer model these two fluids are separated in between by a transition region of linear density variation.

Fresh water and salt water were used to model density stratification in the experiments. The effects of surface wave amplitude and density distribution on the internal motion in the trench were investigated for small density differences compared to the density of water. A new technique using a scanning laser beam and detector system was developed to measure internal wave amplitudes. Satisfactory agreement with the theoretical predictions was obtained. The effects of nonlinearity and viscous dissipation on the internal motions were more pronounced when the depth of the heavier fluid was small compared to the wavelength of the internal waves in the trench.

For a trench in an infinite region, the two-layer model also predicts that large surface wave reflections occur when the trench is "at internal resonance," and a significant portion of the incident wave energy can be dissipated within the trench.

The investigation has provided insight with regard to both the dynamics of wave-trench interaction and the design of navigation channels in density-stratified fluids for reducing the potential of wave-induced internal resonance.

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