Experiments and Numerics of Bichromatic Wave Groups

Abstract

This paper reports on extensive experiments on nonlinear wave groups that evolve in a hydrodynamic laboratory over long distances (200 m) from the generation of simple bichromatic waves. The deepwater experiments show large deformations of the wave group, with large increase of wave heights, depending on the value for the quotient of wave amplitude and frequency difference. The experimental results show little dissipation and reflections are virtually absent. A very efficient and accurate numerical code based on the full nonlinear surface wave equations, which has been developed for this purpose, reconstructs the experiments and enables one to investigate the evolution over much longer distances (reported here until 1,200 m) than in the laboratory.

A σ‐coordinate non‐hydrostatic model with embedded Boussinesq‐type‐like equations for modeling deep‐water waves

“…One can clearly see that the two [37,38]. The interaction/modulation reaches to the maximum at K c x = 275 ∼ 303, where the energy spreads to the lower and higher discrete side-band frequencies.…”

“…In the last decade, a great deal of efforts including laboratory experiments and numerical simulations [36][37][38][39][40][41][42] has been paid to study bi-chromatic waves for better realization of non-linear deep-water physics. Particularly, wave-wave interactions can cause a great deal of energy re-distribution and significantly influence the evolution of deep-water wave groups.…”

Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations

“…In the study, the KdV wave packet which is initially in the bichromatic signals experiences instability deforming the wave and causing an amplitude amplification. Bichromatic wave is formed from a superposition of two monochromatic waves which have same amplitudes and slightly different frequencies [27,30]. This result was obtained by deriving the solution of the KdV equation in the form of asymptotic series up to the third order.…”

“…In a wave tank which initially contains still water, signals are given to the wavemakers generating waves to propagate downstream along the tank. Owing to the nonlinearity effect, the waves deform during their propagation (see [29][30][31][32]). …”

“…However, these two waves' maximum amplitudes are far lower than the amplitude of a wave generated by HUBRIS model although the extreme positions at which the maximum peaking happens conform. HUBRIS model is numerical wave model which was developed based on the Laplace equation (full water equation) [27]. Bichromatic signal deformation was also investigated by employing Boussinesq equation in [24].…”