Spectral description of energy dissipation in breaking wave groups
The dissipation characteristics of laboratory breaking wave groups and random waves are studied. A time-domain eddy viscosity model is used to represent the breaking wave, and the instantaneous dissipation time series deduced from measurements of free surface elevation. Fourier series of these time series yields the dissipation rate as a function of frequency, the frequency dependence of which has been shown to be the inverse of that of the spectral density of free surface elevation for random waves. It is shown that the inverse relationship between the dissipation rate and the free surface spectral density does not appear to hold for wave groups, likely due to the presence of generated long waves in the dissipation time series. These long waves introduce a periodicity into the dissipation time series and inhibit any true randomness from developing. The overall bulk dissipation is calculated from the dissipation rate for both the wave groups and random waves. It appears that, overall, the wave groups undergo a greater degree of dissipation than equivalent random waves.