Experiments on Deep-Water Waves With Two-Dimensional Surface Patterns

Abstract

Experiments are conducted in a three-dimensional wave basin with a wavemaker system comprising 32 side-by-side paddles for which there is precise control. Two types of wavemaker forcings are used to create two-dimensional surface patterns: (1) two symmetric carrier waves interacting at an oblique angle and (2) a single carrier wave propagating in the x-direction with a Jacobi elliptic, sn-function modulation in the y-direction. Data are presented from overhead photographs and from time series obtained by traversing a wave-gage through the patterns. Two parameters are systematically varied: the horizontal aspect ratio of the cells comprising the surface pattern and the measure of nonlinearity of the input wavefield. Unlike such waves in shallow water for which the surface pattern is made up of six-sided cells, the wave pattern for waves in deep water is made up of rectangular cells. Both the overhead photographs and the time series show that for most values of the two parameters, the wavefields evolve with significant modulations in both the x and y directions. In particular, when the aspect ratio of the cells is below about 0.4 for a fixed measure of nonlinearity, there is significant modulation in the y-direction that results in cells with smaller aspect ratios. For aspect ratio above about 0.4, the cells appear to be stable (except for viscous decay) for smaller values of nonlinearity. However, for larger values of nonlinearity even these cells modulate in the y-direction, further increasing the aspect ratio of the evolving cells. For the largest value of nonlinearity considered, the pattern evolves into one that comprises cells with aspect ratios of about 1.