On the growth of water waves and the motions beneath them.

摘要

The fluid zone within half of a wave length of a wavy air-water interface has complex and important flow regimes which are presently neither fully understood nor predictable. This dissertation attempts to increase our understanding in two ways. Firstly, a numerical model of this zone was created and applied to various cases of interest. Secondly, an experiment was conducted to study the active fluid motions beneath the interface in a large laboratory wind-wave facility.;The numerical model describes the fully developed, turbulent, coupled air-water regime and uses the finite difference method for solution. The model is of the linear-instability type, and consists of two main parts, viz., a model of the coupled mean (time-independent) flow profiles in the air and the water, and a model of the time-dependent perturbations to the mean flow caused by the presence of a wave component on the interface. The predictions of the numerical model were compared to a variety of experiments performed in laboratory wave-generation facilities (confined flow) and in the ocean (unconfined flow) and generally demonstrate excellent agreement. The model was also applied to predict momentum and energy transfer across the air-water interface, and the corresponding wave growth rate. In contrast to previous theoretical and numerical models, our model predicts wave growth rates that are in quantitative agreement with both laboratory and field data. In addition, the model can explain the scatter in the field data as being due to variation in surface roughness and flow Reynolds number.;The technique of digital particle image velocimetry (DPIV) was applied to measure instantaneous, two-dimensional velocity fields in the water directly beneath a wavy interface. We studied mechanically-generated waves and wind-generated waves for wind speeds of 1.5, 3.0, 4.5, and 6.0 m/s. Our results confirm the viability and applicability of this technique for the study of motions beneath water waves. Most importantly, the results also show evidence of strong three-dimensional stream-wise circulations beneath the interface at high wind speeds, which cause the sub-surface flow to behave differently in comparison to the flow in the vicinity of a rough, solid boundary.