Abstract
We consider a liquid layer of a finite depth described by Euler’s equations. The ice cover is geometrically modeled by a nonlinear elastic Kirchhoff–Love plate. We determine the trajectories of liquid particles under an ice cover in the field of a nonlinear surface traveling wave rapidly decaying at infinity, namely, a solitary wave packet (a monochromatic wave under the envelope, with the wave velocity equal to the envelope velocity) of a small but finite amplitude. Our analysis is based on the use of explicit asymptotic expressions for solutions describing the wave structures at the water–ice interface of a solitary wave packet type, as well as asymptotic solutions for the velocity field generated by these waves in the depth of the liquid.
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Funding
The research in Sections 1, 2, and 4 was carried out by A. T. Il’ichev, who also participated in the research in Section 3; the research in Section 3 was carried out by A. S. Savin and A. Yu. Shashkov. The work of A. T. Il’ichev was supported by the Russian Science Foundation under grant No. 19-71-30012, https://rscf.ru/en/project/23-71-33002/, at the Steklov Mathematical Institute, Russian Academy of Sciences.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2024, Vol. 218, pp. 586–600 https://doi.org/10.4213/tmf10585.
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Il’ichev, A.T., Savin, A.S. & Shashkov, A.Y. Motion of particles in the field of nonlinear wave packets in a liquid layer under an ice cover. Theor Math Phys 218, 503–514 (2024). https://doi.org/10.1134/S0040577924030097
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DOI: https://doi.org/10.1134/S0040577924030097