Nonlinear and Dissipative Characteristics of a Combined Random-Cnoidal Wave Field

Images of the 2004 Indian Ocean tsunami at landfall shows a leading edge marked by short waves (“fission” waves). These waves appear to be cnoidal in shape and of a temporal and spatial scale in line with the longest swell present in the region, and may interact with the longer waves in the background random wave spectrum. As part of a comprehensive series of experiments, the Large Wave Flume at Oregon State University (USA) was used to generate and measure the properties of cnoidal, random, and combined cnoidal-random wave trains. Both the nonlinear energy transfer characteristics (via bispectral analysis) and dissipation characteristics (via a proxy dissipation function) are studied for all generated wave conditions. It is generally determined that the characteristics of the cnoidal wave dominate the combined cnoidal-random wave signals if the energy of the cnoidal wave is at least equal to that of the random wave.