Effects of Mode Truncation and Dissipation on Predictions of Higher Order Statistics

We investigate the effects mode truncation and dissipation characteristics have on predictions of wave shape statistics such as skewness and asymmetry. We demonstrate the effect of mode truncation by calculating wave shape statistics for data from a laboratory experiment using an increasing number of frequency components each calculation. We find that the values of skewness and asymmetry converge to a maximum as more components are retained, with the maximum values attained when components out to the Nyquist frequency are kept. We run a lowest order Boussinesq shoaling model and a nonlinear dispersive shoaling model with the data, retaining more components with each simulation. Both models show the same convergence characteristics as the data as the number of retained frequency components increases. The lowest order Boussinesq model, despite its shallow water formalism, yields skewness and asymmetry values closer to those of the data than those of the dispersive model. This is likely due to the phase mismatches in the dispersive model, which become large in deep water and thus violate the slowly-varying amplitude assumption. We also investigate the effect of spectral dissipation on these predictions. We run the lowest order Boussinesq shoaling model with different proportions of frequency-dependent dissipation and calculate wave shape statistics. We find that the distribution must take into account some aspect of (f) variation in the dissipation for reliable wave shape statistics.