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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v33.i6.60
pages 567-583

Structure of Nonlinear Wave Packets on the Interface of Liquid Media

Olga V. Avramenko
Kirovograd State V. Vinnichenko Pedagogical University, Kirovograd
Igor T. Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine

ABSTRACT

The paper deals with investigating the amplitudes of higher harmonics in nonlinear wave packets on an interface of liquid media; surface tension is taken into account. Based on a solution obtained by a multiple-scale expansion method, the structure of the packets in the symmetric system "half-space − half-space" and in the asymmetric system "layer − half-space" is studied. It has been established that, unlike the first approximation, each subsequent one determines the amplitude of the respective higher harmonic only approximately, and at the same time it makes corrections to the amplitude of each preceding harmonic. The third-approximation solution reveals the existence of an extreme value of the higher-harmonic amplitudes at certain values of the first harmonic's length and the layer's thickness. The dependence of the wave packet's shape vs the surface tension and the ratio between the height and the length of the first harmonic has been found out.