Experimental Investigations of Capillary Effects on Nonlinear Free-Surface Waves

Abstract

This thesis presents the results of three experiments on various aspects of the effects of surface tension on nonlinear free-surface waves. The first two experiments focus on capillary effects on the breaking of short-wavelength gravity waves, a problem of interest in areas of physical oceanography and remote sensing. The third experiment is concerned with the bifurcation of solitary capillary-gravity waves, a problem that is relevant in the study of nonlinear, dispersive wave systems. In the first set of experiments, streamwise profile measurements were made of spilling breakers at the point of incipient breaking. Both wind-waves and mechanically generated waves were investigated in this study, with gravity wavelengths in the range of 10--120 cm. Although it has been previously argued that the crest shape is dependent only on the surface tension, the results reported herein are to the contrary as several geometrical parameters used to describe the crest change significantly with the wavelength. However, the non-dimensional crest shape is self-similar, with two-shape parameters that depend on a measure of the local wave slope. This self-similarity persists over the entire range of wavelengths and breaker conditions measured, indicating a universal behavior in the near-crest dynamics that is independent of the method used to generate the wave. The measured wave slope is found to be related to the wave growth rate and phase-speed prior to breaking, a result that contributes towards the development of a breaking criterion for unsteady capillary-gravity waves. The second set of experiments examines the cross-stream surface structure in the turbulent breaking zone generated by short-wavelength breakers. Waves in this study were generated using a mechanical wedge and ranged in wavelength from 80--120 cm. To isolate the effects of surface tension on the flow, the important experimental parameters were adjusted to produce Froude-scaled, dispersively-focused wave packets. The results show the development of quasi''-2D streamwise ripples along with smaller cross-stream ripples that grow as breaking develops and can become comparable in amplitude to the streamwise ripples for larger breakers. It is found that the amplitude of the cross-stream surface ripples scale as $\bar{&lambda}^3$, where $\bar{&lambda}$ is the average wavelength of the wave packet. The cross-stream ripple activity appears to be highest in the troughs'' of the larger streamwise ripples, with the appearance of persistent ``scar''-like features. Based on these observations, a simple model for the coupling between the vorticity and capillary structure in the breaking zone is conjectured. The third set of experiments focuses on the generation of capillary-gravity waves by a pressure source moving near the minimum phase speed cmin. Near this minimum, nonlinear capillary-gravity solitary waves, or lumps'', have been shown to exist theoretically. We identify an abrupt transition to a wave-like state that features a localized solitary wave that trails the pressure forcing. This trailing wave is steady, fully localized in 3D, elongated in the cross-stream relative to the streamwise direction, and has a one-to-one relationship between height and phase speed. All of these characterisitics are commensurate with the freely propogating lumps'' computed by previous authors, and a quantitative comparison between these previous numerical calculations and the current experiments is presented. At speeds closer to cmin, a new time-dependent state is observed that can qualitatively be described by the shedding of solitary depressions from the tips of a ``V''-shaped pattern. These results are discussed in conjunction with a new theoretical model for these waves that employs nonlinear and viscous effects, both of which are crucial in capturing the salient features of the surface response. While discussed in the context of water waves, these results have applicaiton to other wave systems where nonlinear and dispersive effects are important.