Estimation of incident and reflected components in highly nonlinear regular waves

Separation of Long-Crested Nonlinear Bichromatic Waves into Incident and Reflected Components

“…Lykke Andersen et al [7] showed that for regular waves the celerity of the bound superharmonics is higher than a free component at the same frequency, and this makes it possible to separate the bound and free waves. The same applies to bichromatic waves, and thus for bichromatic waves it is also possible to separate the bound and free superharmonic components due to their different celerities.…”

“…Later, an iterative procedure to estimate the wave numbers will be presented. The amplitudes are then calculated by a least-squares approach identical to that used by Lykke Andersen et al [7] for regular waves.…”

“…where k f is the wave number of the free waves at the cyclic frequency ω i and is calculated by the linear dispersion equation. The amplitudes of the bound harmonics can also be calculated by a least-square method when the wave numbers are known (see solution in Lykke Andersen et al [7]).…”

“…The nonlinear LASA methods (Local Approximation using Simulated Annealing) by Figueres et al [5] and Figueres and Medina [6] are based on local time domain solutions fitted to theoretical wave profiles, making application of their method to cases where free energy exists questionable. Even when no free energy exists and even for linear waves, Lykke Andersen et al [7] and Eldrup and Lykke Andersen [8] found that the LASA V method was not accurate, and as the method at the same time is computationally very expensive, it is not practical for real applications.…”

“…Recently, a nonlinear frequency domain method to separate regular waves into incident and reflected components was developed, cf. Lykke Andersen et al [7]. This method is an extension of the Lin and Huang [4] method, but includes amplitude dispersion based on stream function wave theory (Fenton and Rienecker [9]).…”