Phase Structure of Fluid Fluctuations with a Floating Elastic Ice Plate under Nonlinear Interaction of Progressive Surface Waves

A. E. Bukatov, A. A. Bukatov^✉

Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation

^✉ e-mail: newisland@list.ru

Abstract

Asymptotic expansions up to the third-order terms are constructed based on the multiple scales method for the fluid velocity potential of the finite-depth homogeneous fluid and elevation of the plate-fluid surface (ice-water surface). The obtained expansions constitute a foundation for analyzing dispersive properties of the fluctuations formed under interaction of progressive harmonics of the finite-amplitude surface waves. Changes of the fluctuation frequency taking place due to the contribution of the values of the first and second approximations conditioned by the taken into account non-linearity are considered. The effect of non-linearity of the ice plate vertical displacement acceleration on the amplitude, frequency and phase velocity of the wave disturbances is studied. It is shown that at the wave numbers exceeding the maximum resonance value, the oscillation frequency increases in case non-linearity of the plate vertical displacement acceleration is taken into account. It also grows with the plate thickness, and change of a sign (plus into minus) of the second interacting harmonic amplitude reduces the frequency value if the wave number is fixed. The phase velocity increase with allowance for the acceleration nonlinearity is more significant than without considering it. Under a negative amplitude of the second interacting harmonic, if the acceleration nonlinearity is taken into account, the phase velocity is less than when it is not.

Keywords

ice plate fluctuations, waves of finite amplitude, nonlinear interaction of waves, flexural deformation of plate, phase characteristics

Acknowledgements

The present study is carried out within the framework of the State Order No. 0827-2018-0003.

Original russian text

Original Russian Text © A. E. Bukatov, A. A. Bukatov, 2018, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 34, Iss. 1, pp. 5–19 (2018)

For citation

Bukatov, A.E. and Bukatov, A.A., 2018. Phase Structure of Fluid Fluctuations with a Floating Elastic Ice Plate under Nonlinear Interaction of Progressive Surface Waves. Physical Oceanography, (1), pp. 3-17. doi:10.22449/1573-160X-2018-1-3-17

DOI

10.22449/1573-160X-2018-1-3-17

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