Marwan Ramli, Said Munzir, T. Khairuman, Vera Halfiani
Previous analytical, numerical and experimental results show that surface waves which initially bichromatic signals deform during their propagation in hydrodynamic laboratories. The deformation is followed by the increase of the bichromatic wave amplitude. It has been investigated that the position where the bichromatic wave generates the highest amplitude is of order O(1/q2, 1/κlin2) where q and κlin are the amplitude and frequency of the bichromatic wave envelope, respectively. The result is based on the third order Korteweg de Vries (KdV) equation and the quantity obtained is called maximal temporal amplitude (MTA). However, the dependence of the increase in the maximum amplitude of the bichromatic wave over wave parameters is unknown. This paper describes the derivation of a formula that can be used to predict the increase of the maximum amplitude of bichromatic wave. Here, the bichromatic wave is defined as a superposition of two monochromatic waves with the same amplitude but slightly different of frequencies. The formula is derived using the approximation of fifth order KdV equation and MTA. It has been found that the increase of a bichromatic wave maximum amplitude is of order O(q/κlin)2. The result of the increase of maximum amplitude for bichromatic wave found using this formula is in accordance with the experimental results as well as the result of a numerical software HUBRIS. © 2014 Pushpa Publishing House, Allahabad, India.
Department of Mathematics, Syiah Kuala University, Banda Aceh, 23111, Indonesia; Dynamic Application and Optimization Groups, Syiah Kuala University, Banda Aceh, 23111, Indonesia; Department of Physics, Syiah Kuala University, Banda Aceh, 23111, Indonesia; Syiah Kuala University, Banda Aceh, 23111, Indonesia
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