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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

REFERENCES

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards.Google Scholar
Bukatov, A. E. 1980 Influence of a longitudinally compressed elastic plate on the non-stationary wave motion of a homogeneous liquid. Fluid Dyn. 15 (5), 687–693.CrossRefGoogle Scholar
Bukatov, A. E. 2017 Waves in a Sea with a Floating Ice Cover [in Russian]. Marine Hydrophysical Institute of RAS.Google Scholar
Chakrabarti, A. & Mohapatra, S. 2013 Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth. J. Mar. Sci. Appl. 12, 325–333.CrossRefGoogle Scholar
Das, D. & Sahu, M. 2019 Wave radiation by a horizontal circular cylinder submerged in deep water with ice-cover. J. Ocean Engng Sci. 4, 49–54.CrossRefGoogle Scholar
Das, S., Kar, P., Sahoo, T. & Meylan, M. H. 2018 a Flexural-gravity wave motion in the presence of shear current: wave blocking and negative energy waves. Phys. Fluids 30, 106606.CrossRefGoogle Scholar
Das, S., Sahoo, T. & Meylan, M. H. 2018 b Dynamics of flexural gravity waves: from sea ice to hawking radiation and analogue gravity. Proc. R. Soc. Lond. A 474, 20170223.Google ScholarPubMed
Das, S., Sahoo, T. & Meylan, M. H. 2018 c Flexural-gravity wave dynamics in two-layer fluid: blocking and dead water analogue. J. Fluid Mech. 854, 121–145.CrossRefGoogle Scholar
Davys, J. W., Hosking, R. J. & Sneyd, A. D. 1987 Waves due to a steadily moving source on a floating ice plate. J. Fluid Mech. 180, 297–318.Google Scholar
Eatock Taylor, R. & Hu, C. S. 1991 Multipole expansions for wave diffraction and radiation in deep water. Ocean Engng 18 (3), 191–224.CrossRefGoogle Scholar
Il'ichev, A. T., Savin, A. A. & Savin, A. S. 2012 Formation of wave on an ice-sheet above the dipole, moving in a fluid. Dokl. Phys. 57, 202–205.CrossRefGoogle Scholar
Il'ichev, A. T. & Savin, A. S. 2017 Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column. Theor. Math. Phys. 193 (3), 1801–1810.CrossRefGoogle Scholar
Kheisin, D. Ye. 1967 Dynamics of Floating Ice Cover [in Russian. Technical English Translation in: FSTC-HT-23-485-69, U.S. Army Foreign Science and Technology Center].Google Scholar
Krasil'nikov, V. N. 1962 On excitation of flexural-gravity waves. Akust. Zh. 8, 133–136.Google Scholar
Li, Z. F., Wu, G. X. & Ji, C. Y. 2018 Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack. J. Fluid Mech. 845, 682–712.CrossRefGoogle Scholar
Li, Z. F., Wu, G. X. & Shi, Y. Y. 2019 Interaction of uniform current with a circular cylinder submerged below an ice sheet. Appl. Ocean Res. 86, 310–319.CrossRefGoogle Scholar
Linton, C. M. & McIver, P. 2001 Handbook of Mathematical Techniques for Wave/Structure Interactions. CRC Press.CrossRefGoogle Scholar
Liu, A. K. & Mollo-Christensen, E. 1988 Wave propagation in a solid ice pack. J. Phys. Oceanogr. 18, 1702–1712.2.0.CO;2>CrossRefGoogle Scholar
Pavelyeva, E. B. & Savin, A. S. 2018 Establishment of waves generated by a pulsating source in a finite-depth fluid. Fluid Dyn. 53, 461–470.CrossRefGoogle Scholar
Sahoo, T. 2012 Mathematical Techniques for Wave Interaction with Flexible Structures. CRC Press.CrossRefGoogle Scholar
Savin, A. A. & Savin, A. S. 2012 Ice cover perturbation by a dipole in motion within a liquid. Fluid Dyn. 47 (2), 139–146.CrossRefGoogle Scholar
Savin, A. A. & Savin, A. S. 2013 Waves generated on an ice cover by a source pulsating in fluid. Fluid Dyn. 48, 303–309.CrossRefGoogle Scholar
Savin, A. A. & Savin, A. S. 2015 Three-dimensional problem of disturbing an ice cover by a dipole moving in fluid. Fluid Dyn. 50, 613–620.CrossRefGoogle Scholar
Schulkes, R. M. S. M., Hosking, R. J. & Sneyd, A. D. 1987 Waves due to a steadily moving source on a floating ice plate. Part 2. J. Fluid Mech. 180, 297–318.CrossRefGoogle Scholar
Squire, V. A. 2008 Synergies between VLFS hydroelasticity and sea-ice research. Intl J. Offshore Polar Engng 18, 1–13.Google Scholar
Squire, V. A., Hosking, R. J., Kerr, A. D. & Langhorne, P. J. 1996 Moving Loads on Ice Plates. Kluwer Academic Publishers.CrossRefGoogle Scholar
Sturova, I. V. 2013 Unsteady three-dimensional sources in deep water with an elastic cover and their applications. J. Fluid Mech. 730, 392–418.CrossRefGoogle Scholar