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Hydroelastic waves propagating in an ice-covered channel

Published online by Cambridge University Press:  14 January 2020

K. Ren ,
G. X. Wu Open the ORCID record for G. X. Wu [Opens in a new window]  and
Z. F. Li
K. Ren
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 7JE, UK
G. X. Wu*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 7JE, UK
Z. F. Li
Affiliation:
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang212003, China
*
†Email address for correspondence: g.wu@ucl.ac.uk
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Abstract

The hydroelastic waves in a channel covered by an ice sheet, without or with crack and subject to various edge constraints at channel banks, are investigated based on the linearized velocity potential theory for the fluid domain and the thin-plate elastic theory for the ice sheet. An effective analytical solution procedure is developed through expanding the velocity potential and the fourth derivative of the ice deflection to a series of cosine functions with unknown coefficients. The latter are integrated to obtain the expression for the deflection, which involves four constants. The procedure is then extended to the case with a longitudinal crack in the ice sheet by using the Dirac delta function and its derivatives at the crack in the dynamic equation, with unknown jumps of deflection and slope at the crack. Conditions at the edges and crack are then imposed, from which a system of linear equations for the unknowns is established. From this, the dispersion relation between the wave frequency and wavenumber is found, as well as the natural frequency of the channel. Extensive results are then provided for wave celerity, wave profiles and strain in the ice sheet. In-depth discussions are made on the effects of the edge condition, and the crack.

JFM classification

Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A18
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Andrianov, A. I. & Hermans, A. J. 2003 The influence of water depth on the hydroelastic response of a very large floating platform. Mar. Struct. 16 (5), 355–371.CrossRefGoogle Scholar
Balmforth, N. J. & Craster, R. V. 1999 Ocean waves and ice sheets. J. Fluid Mech. 395, 89–124.CrossRefGoogle Scholar
Batyaev, E. A. & Khabakhpasheva, T. I. 2015 Hydroelastic waves in a channel covered with a free ice sheet. Fluid Dyn. 50 (6), 775–788.CrossRefGoogle Scholar
Bauer, H. F. 1993 Frequencies of a hydroelastic rectangular system. Forsch. Ing. Wes. 59 (1–2), 18–28.CrossRefGoogle Scholar
Beltaos, S. 2004 Wave-generated fractures in river ice covers. Cold Reg. Sci. Technol. 40 (3), 179–191.CrossRefGoogle Scholar
Chang, P., Melville, W. K. & Miles, J. W. 1979 On the evolution of a solitary wave in a gradually varying channel. J. Fluid Mech. 95 (3), 401–414.CrossRefGoogle Scholar
Chung, H. & Fox, C. 2002 Calculation of wave–ice interaction using the Wiener–Hopf technique. New Zealand J. Math. 31 (1), 1–18.Google Scholar
Daly, S. F. 1993 Wave propagation in ice-covered channels. ASCE J. Hydraul. Engng 119 (8), 895–910.CrossRefGoogle Scholar
Daly, S. F. 1995 Fracture of river ice covers by river waves. J. Cold Reg. Engng 9 (1), 41–52.CrossRefGoogle Scholar
Dolatshah, A., Nelli, F., Bennetts, L. G., Alberello, A., Meylan, M. H., Monty, J. P. & Toffoli, A. 2018 Hydroelastic interactions between water waves and floating freshwater ice. Phys. Fluids 30 (9), 091702.CrossRefGoogle Scholar
Ertekin, R. C., Webster, W. C. & Wehausen, J. V. 1986 Waves caused by a moving disturbance in a shallow channel of finite width. J. Fluid Mech. 169, 275–292.CrossRefGoogle Scholar
Evans, D. V. & Porter, R. 2003 Wave scattering by narrow cracks in ice sheets floating on water of finite depth. J. Fluid Mech. 484, 143–165.CrossRefGoogle Scholar
Evans, D. V. & Davies, T. V.1968 Wave–ice interaction. Tech. Rep. Stevens Institute of Technology, Hoboken NJ, Davidson Lab.Google Scholar
Fox, C. & Squire, V. A. 1990 Reflection and transmission characteristics at the edge of shore fast sea ice. J. Geophys. Res. 95 (C7), 11629–11639.CrossRefGoogle Scholar
Fox, C. & Squire, V. A. 1994 On the oblique reflexion and transmission of ocean waves at shore fast sea ice. Phil. Trans. R. Soc. Lond. A 347 (1682), 185–218.Google Scholar
Fuamba, M., Bouaanani, N. & Marche, C. 2007 Modeling of dam break wave propagation in a partially ice-covered channel. Adv. Water Resour. 30 (12), 2499–2510.CrossRefGoogle Scholar
Korobkin, A. A., Khabakhpasheva, T. I. & Papin, A. A. 2014 Waves propagating along a channel with ice cover. Eur. J. Mech. (B/Fluids) 47, 166–175.CrossRefGoogle Scholar
Li, Z. F., Wu, G. X. & Shi, Y. Y. 2018 Wave diffraction by a circular crack in an ice sheet floating on water of finite depth. Phys. Fluids 30 (11), 117103.CrossRefGoogle Scholar
Linton, C. M. & Evans, D. V. 1992 The radiation and scattering of surface waves by a vertical circular cylinder in a channel. Phil. Trans. R. Soc. Lond. A 338 (1650), 325–357.Google Scholar
Manam, S. R., Bhattacharjee, J. & Sahoo, T. 2006 Expansion formulae in wave structure interaction problems. Proc. R. Soc. Lond. A 462 (2065), 263–287.CrossRefGoogle Scholar
Mathew, J. & Akylas, T. R. 1990 On three-dimensional long water waves in a channel with sloping sidewalls. J. Fluid Mech. 215, 289–307.CrossRefGoogle Scholar
Meylan, M. H. & Squire, V. A. 1996 Response of a circular ice floe to ocean waves. J. Geophys. Res. 101 (C4), 8869–8884.CrossRefGoogle Scholar
Mondal, R., Mohanty, S. K. & Sahoo, T. 2011 Expansion formulae for wave structure interaction problems in three dimensions. IMA J. Appl. Maths 78 (2), 181–205.CrossRefGoogle Scholar
Myland, D. & Ehlers, S. 2019 Investigation on semi-empirical coefficients and exponents of a resistance prediction method for ships sailing ahead in level ice. Ships Offshore Struct. 14 (sup. 1), 161–170.CrossRefGoogle Scholar
Nzokou, F., Morse, B. & Quach-Thanh, T. 2009 River ice cover flexure by an incoming wave. Cold Reg. Sci. Technol. 55 (2), 230–237.CrossRefGoogle Scholar
Nzokou, F., Morse, B., Robert, J.-L., Richard, M. & Tossou, E. 2011 Water wave transients in an ice-covered channel. Can. J. Civil Engng 38 (4), 404–414.CrossRefGoogle Scholar
Porter, R. 2019 The coupling between ocean waves and rectangular ice sheets. J. Fluids Struct. 84, 171–181.CrossRefGoogle Scholar
Porter, R. & Evans, D. V. 2006 Scattering of flexural waves by multiple narrow cracks in ice sheets floating on water. Wave Motion 43 (5), 425–443.CrossRefGoogle Scholar
Porter, R. & Evans, D. V. 2007 Diffraction of flexural waves by finite straight cracks in an elastic sheet over water. J. Fluids Struct. 23 (2), 309–327.CrossRefGoogle Scholar
Sahoo, T., Yip, T. L. & Chwang, A. T. 2001 Scattering of surface waves by a semi-infinite floating elastic plate. Phys. Fluids 13 (11), 3215–3222.CrossRefGoogle Scholar
Squire, V. A. 2020 Ocean wave interactions with sea ice: a reappraisal. Annu. Rev. Fluid Mech. 52, 37–60.CrossRefGoogle Scholar
Squire, V. A. & Dixon, T. W. 2000 An analytic model for wave propagation across a crack in an ice sheet. Intl J. Offshore Polar Engng 10 (03), 173–176.Google Scholar
Timoshenko, S. P. & Woinowsky-Krieger, S. 1959 Theory of Plates and Shells. McGraw-Hill.Google Scholar
Wang, J. & Qiao, P. 2007 Vibration of beams with arbitrary discontinuities and boundary conditions. J. Sound Vib. 308 (1–2), 12–27.CrossRefGoogle Scholar
Winckler, P. & Liu, P. L.-F. 2015 Long waves in a straight channel with non-uniform cross-section. J. Fluid Mech. 770, 156–188.CrossRefGoogle Scholar
Witting, J. M. 1984 A unified model for the evolution nonlinear water waves. J. Comput. Phys. 56 (2), 203–236.CrossRefGoogle Scholar
Wu, G. X. 1998 Wave radiation and diffraction by a submerged sphere in a channel. Q. J. Mech. Appl. Maths 51 (4), 647–666.CrossRefGoogle Scholar
Xia, X. & Shen, H. T. 2002 Nonlinear interaction of ice cover with shallow water waves in channels. J. Fluid Mech. 467, 259–268.CrossRefGoogle Scholar