Effect of combination of dispersion and non linear term to downstream running nonlinear water waves

MARWAN RAMLI, T. KHAIRUMAN3, SAID MUNZIR

Abstract


This paper discuss the impact of dispersion and non-linear terms combinations the surface wave equation particularly on the peaking phenomena of the wave water that initially in the form of a bichromatic wave. The study for both of these terms are focused on the position where the bichromatic wave experience its highest peaking and its related bichromatic amplitude amplification. In the previous study, the position where the bichromatic wave experience its highest peaking is of order   and its bichromatic amplitude amplification is of order , where  and  are the amplitude and frequency of the bichromatic wave envelope, respectively. This result is based on the fifth order Korteweg de Vries (KdV) equation and the quantity that obtained is called Maximal Temporal Amplitude (MTA). However, despite the the position where the bichromatic wave experience its highest peaking suits the result  of Stansberg experiment and the result of numerical calculation using HUBRIS, its related bichromatic wave amplitude amplification is not close enough. The source of this discrepancy is suspected from the dispersion and non-linear terms of the KdV equation used. This study shows that the existence of the dispersion and non-linear terms influences the position of  Maximal Temporal Amplitude (MTA) and its bichromatic wave amplitude amplification.  For the coefficient of dispersion term of 1.0065 and  nonlinear term of , the position of MTA and bichromatic wave amplitude amplification suits the result of Stansberg experiment and the result of numerical calculation using HUBRIS

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