No abstract

Modeling of wave energy transformation and breaking on fringing reefs is inherently difficult due to their unique topography. Prior methods of determining dissipation are based on empirical data from gently sloping beaches and offer only bulk energy dissipation estimates over the entire spectrum. Methods for deducing a frequency dependent dissipation have been limited to hypothesized linkages between dissipation and wave shape in the surf, and have used bulk dissipation models as a constraint on the overall dissipation for mild sloping beaches. However, there is no clear indication that the constraint on the overall level of dissipation is suitable for the entire reef structure. Using these constraints the frequency dependent dissipation rate can be deduced from laboratory data, taken at the Coastal and Hydraulics Laboratory, of wave transformation over reefs. The frequency dependent dissipation rate can then be integrated over the spectrum to derive an empirically-based counterpart to energy flux dissipation. Comparing the bulk energy dissipation estimates for the reef system to the frequency based method allows for the modification of wave breaking parameters in the frequency estimation, to better estimate total dissipation. Since this method is based on the Fourier transform of the time series data, it allows the dissipation to be found as a function of the frequency. This analysis shows that there is a correlation between the amount of energy in the low frequencies of the wave spectrum and certain characteristics of the frequency dependent dissipation coefficient.

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.

The dissipation and nonlinear effects of random swell interaction with transient long waves are studied. Results from a laboratory experiment in which random swell was generated both with and without a co-existing transient long wave are analyzed. An instantaneous dissipation mechanism for estimating both instantaneous and bulk dissipation from data is used to determine the characteristics of dissipation for both cases. Fourier analysis of the free surface measurements and dissipation estimates reveals that the presence of the transient long wave does not have an appreciable impact on the known dissipation characteristics of random swell. However, the use of wavelet analysis, centered on the long wave in the time series, shows that the dissipation characteristics of the combined short-long wave signals deviate considerably from that of swell alone, indicating that smearing of the long wave signal by the Fourier analysis is sufficiently strong to affect dissipation estimates. A wavelet-based bispectral algorithm is used to determine the nonlinear wave-wave coupling in both swell and combined swell-long wave signals; the results indicate that there can be broader ranges of frequencies in which nonlinear coupling is present for the case of the combined short-long wave signal.