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Waves on a compressed floating ice plate caused by motion of a dipole in water

Published online by Cambridge University Press:  24 November 2020

Yury A. Stepanyants Open the ORCID record for Yury A. Stepanyants [Opens in a new window]  and
Izolda V. Sturova
Yury A. Stepanyants*
Affiliation:
School of Sciences, University of Southern Queensland, Toowoomba, Queensland4350, Australia Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod603950, Russia
Izolda V. Sturova
Affiliation:
Lavrentyev Institute of Hydrodynamics of Siberian Branch of Russian Academy of Sciences, Novosibirsk630090, Russia
*
†Email address for correspondence: yury.stepanyants@usq.edu.au
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Abstract

In the linear approximation, we study wave motions of a compressed elastic ice sheet caused by the motion of a two-dimensional dipole in the water beneath the sheet. The fluid flow is described by the potential theory, while the ice sheet is modelled through a thin elastic plate floating on the water surface. The solution for the vertical displacement of the ice sheet is derived for a transient dipole undergoing arbitrary two-dimensional motion. Three cases are considered in detail when the dipole moves horizontally with a uniform speed at some depth or horizontally oscillates, or moves and oscillates. The formulae for the plate displacement are derived for the fluid of finite depth, but then analysed in detail for the infinitely deep case. We show that the character of the solutions is different in the different domains of the parameter plane and classify the possible cases. Then we calculate the wave patterns on the plate for the different regimes of dipole motion and typical values of plate parameters. The studied problem can be considered as the simplified model of motion of a circular cylinder in a water under an ice cover. In the last section we compare the characteristics of wave motions onsetting in the far-field zone of the flow around a circular cylinder and its dipole approximation and show that the difference in the wave characteristics and force loads for these two cases is small and quickly vanishes when the ice plate thickness increases. In conclusion, we present estimates of amplitudes and wavelengths of wave perturbations for the real oceanic conditions.

JFM classification

Geophysical and Geological Flows: Ice sheets Geophysical and Geological Flows: Ocean processes Waves/Free-surface Flows: Elastic waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A7
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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