Statistical behaviour of directional bound long waves

The statistical behaviour of bound long waves is deduced from numerical simulations carried out starting from local spectra derived from deep-water directional specta. The investigation refers both to the time and space domain, in the directions of wave fronts, that is alongshore if an head on attach towards a uniform beach is considered. The values of the heights, periods and front lengths of the bound long waves are obtained and compared with those of the nonlinear waves associated with the complete second order local spetra. The influence of the directional energy spreading is examined, wich seems to affect the periods and lenghts of the wave fronts more than the heights of the bound long waves. The numerical results of the analysis carried out in a coastal region and illustrated here with reference to field cases from Bowers (1992) show the following: the energy density of the bound long waves increases as the depth decreases, being, in any case, about 10% of the local energy density associated with the complete second order spectra; the spectral mean periods referred to the bound long waves exhibit an increasing trend in decreasing depth; the characteristic lengths of the wave fronts assume quite the same values whatever the depth. The last result suggests that beach configurations induced by bound long waves are affected by the features exhibited by the bound long waves approaching the coastal region, which depend on the deep-water wave climate rather than on the modification experienced during the shoreward propagation.