Physical parameters of solitary wave packets in shallow basins under ice cover
A. T. Il'ichev
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
We determine the velocities and lengths of solitary envelope waves whose velocity is located in a left half-neighborhood of the phase velocity minimum in the dispersion relation for shallow basins under ice cover. The ice cover is modeled as an elastic Kirchhoff–Love ice plate. The Euler equation for the liquid layer (water) includes an additional pressure from the plate, which floats freely on the liquid surface. We consider the case of weakly nonlinear waves in the limit of long wavelengths and small amplitudes where the initial dimensionless stress in the ice cover does not exceed one third. These waves are described by a fifth-order Kawahara equation. We then compare the obtained results with the parameters found using a strongly nonlinear description. The comparison yields very good results for shallow depths of the considered basin. This phenomenon is explained by the properties of the lowest nonlinearity coefficient in the equations describing the solitary envelope waves branching from the phase velocity minimum on the dispersion curve. We discuss possible applications of the obtained results to experimental wave measurements under an ice cover.
ice cover, solitary envelope wave, bifurcation, nonlinear Schrödinger equation, equation in quasinormal form.
|Russian Science Foundation
|This research was supported by a grant from the Russian Science Foundation (Project No. 19-71-30012).
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Theoretical and Mathematical Physics, 2019, 201:3, 1710–1722
A. T. Il'ichev, “Physical parameters of solitary wave packets in shallow basins under ice cover”, TMF, 201:3 (2019), 347–360; Theoret. and Math. Phys., 201:3 (2019), 1710–1722
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\paper Physical parameters of solitary wave packets in shallow basins under ice cover
\jour Theoret. and Math. Phys.
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