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Interactions of waves with a body floating in an open water channel confined by two semi-infinite ice sheets

Published online by Cambridge University Press:  23 April 2021

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

Wave radiation and diffraction problems of a body floating in an open water channel confined by two semi-infinite ice sheets are considered. The linearized velocity potential theory is used for fluid flow and a thin elastic plate model is adopted for the ice sheet. The Green function, which satisfies all the boundary conditions apart from that on the body surface, is first derived. This is obtained through applying Fourier transform in the longitudinal direction of the channel, and matched eigenfunction expansions in the transverse plane. With the help of the derived Green function, the boundary integral equation of the potential is derived and it is shown that the integrations over all other boundaries, including the bottom of the fluid, free surface, ice sheet, ice edge as well as far field will be zero, and only the body surface has to be retained. This allows the problem to be solved through discretization of the body surface only. Detailed results for hydrodynamic forces are provided, which are generally highly oscillatory owing to complex wave–body–channel interaction and body–body interaction. In depth investigations are made for the waves confined in a channel, which does not decay at infinity. Through this, a detailed analysis is presented on how the wave generated by a body will affect the other bodies even when they are far apart.

JFM classification

Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abramowitz, M. & Stegun, I.A. 1965 Handbook of Mathematical Functions. Dover Press.Google Scholar
Appolonov, E.M., Sazonov, K.E., Dobrodeev, A.A., Klementieva, N.Y., Kudrin, M.A., Maslich, E.A., Petinov, V.O. & Shaposhnikov, V.M. 2013 Studies for development of technologies to make a wide channel in ice. In The 22nd International Conference on Port and Ocean Engineering under Arctic Conditions. 9–13 June, Espoo, Finland.Google Scholar
Bennetts, L.G. & Williams, T.D. 2010 Wave scattering by ice floes and polynyas of arbitrary shape. J. Fluid Mech. 662, 5–35.CrossRefGoogle Scholar
Chung, H. & Linton, C.M. 2005 Reflection and transmission of waves across a gap between two semi-infinite elastic plates on water. Q. J. Mech. Appl. Maths 58, 1–15.CrossRefGoogle Scholar
Eatock Taylor, R. & Hung, S.M. 1985 Mean drift forces on an articulated column oscillating in a wave tank. Appl. Ocean Res. 7, 66–78.CrossRefGoogle Scholar
Erdélyi, A. 1953 Higher Transcendental Functions. McGraw-Hill.Google Scholar
Lee, C.H., Newman, J.N. & Zhu, X. 1996 An extended boundary integral equation method for the removal of irregular frequency effects. Intl J. Numer. Meth. Fluids 23, 637–660.3.0.CO;2-3>CrossRefGoogle Scholar
Li, Z.F., Shi, Y.Y. & Wu, G.X. 2017 Interaction of wave with a body floating on a wide polynya. Phys. Fluids 29, 097104.CrossRefGoogle Scholar
Li, Z.F., Shi, Y.Y. & Wu, G.X. 2018 a Interaction of waves with a body floating on polynya between two semi-infinite ice sheets. J. Fluids Struct. 78, 86–108.CrossRefGoogle Scholar
Li, Z.F., Shi, Y.Y. & Wu, G.X. 2020 a A hybrid method for linearized wave radiation and diffraction problem by a three dimensional floating structure in a polynya. J. Comput. Phys. 412, 109445.CrossRefGoogle Scholar
Li, Z.F., Wu, G.X. & Ji, C.Y. 2018 b 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. & Ren, K. 2020 b Wave diffraction by multiple arbitrary shaped cracks in an infinitely extended ice sheet of finite water depth. J. Fluid Mech. 893, A14.CrossRefGoogle Scholar
Li, Z.F., Wu, G.X. & Shi, Y.Y. 2018 c Wave diffraction by a circular crack in an ice sheet floating on water of finite depth. Phys. Fluids 30, 117103.CrossRefGoogle Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Linton, C.M. 1999 A new representation for the free-surface channel Green's function. Appl. Ocean Res. 21, 17–25.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, 325–357.Google Scholar
Newman, J.N. 1977 Marine Hydrodynamics. MIT Press.CrossRefGoogle Scholar
Newman, J.N. 2016 Channel wall effects in radiation-diffraction analysis. In The 31st International Workshop on Water Waves and Floating Bodies. 3–6 April, Plymouth, USA.Google Scholar
Newman, J.N. 2017 Trapped-wave modes of bodies in channels. J. Fluid Mech. 812, 178–198.CrossRefGoogle Scholar
Porter, R 2018 Trapping of waves by thin floating ice floes. Q. J. Mech. Appl. Maths 71, 463–483.Google Scholar
Ren, K., Wu, G.X. & Ji, C.Y. 2018 Wave diffraction and radiation by a vertical circular cylinder standing in a three-dimensional polynya. J. Fluids Struct. 82, 287–307.CrossRefGoogle Scholar
Ren, K., Wu, G.X. & Thomas, G.A. 2016 Wave excited motion of a body floating on water confined between two semi-infinite ice sheets. Phys. Fluids 28, 127101.CrossRefGoogle Scholar
Riska, K., Lohi, P. & Eronen, H. 2005 The width of the channel achieved by an azimuth thruster icebreaker. In The 18th International Conference on Port and Ocean Engineering under Arctic Conditions. 26–30 June, New York, USA.Google Scholar
Robin, G.Q. 1963 Wave propagation through fields of pack ice. Phil. Trans. R. Soc. Lond. A 255, 313–339.Google Scholar
Squire, V.A. 2011 Past, present and impendent hydroelastic challenges in the polar and subpolar seas. Phil. Trans. R. Soc. Lond. A 369, 2813–2831.Google ScholarPubMed
Squire, V.A., Dugan, J.P., Wadhams, P., Rottier, P.J. & Liu, A.K. 1995 Of ocean waves and sea ice. Annu. Rev. Fluid Mech. 27, 115–168.CrossRefGoogle Scholar
Squire, V.A., Robinson, W.H., Langhorne, P.J. & Haskell, T.G. 1988 Vehicles and aircraft on floating ice. Nature 333, 159–161.CrossRefGoogle Scholar
Srokosz, M.A. & Evans, D.V. 1979 A theory for wave-power absorption by two independently oscillating bodies. J. Fluid Mech. 90, 337–362.CrossRefGoogle Scholar
Sturova, I.V. 2015 Radiation of waves by a cylinder submerged in water with ice floe or polynya. J. Fluid Mech. 784, 373–395.CrossRefGoogle Scholar
Timoshenko, S.P. & Woinowsky, K.S. 1959 Theory of Plates and Shells. McGraw-Hill.Google Scholar
Ursell, F. 1951 Trapping modes in the theory of surface waves. Math. Proc. Camb. Phil. Soc. 47, 347–358.CrossRefGoogle Scholar
Ursell, F. 1999 On the wave motion near a submerged sphere between parallel walls: I. Multipole potentials. Q. J. Mech. Appl. Maths 52, 585–604.CrossRefGoogle Scholar
Wehausen, J.V. & Laitone, E.V. 1960 Surface Waves, pp. 446–778. Springer.Google Scholar
Williams, T.D. & Squire, V.A. 2006 Scattering of flexural–gravity waves at the boundaries between three floating sheets with applications. J. Fluid Mech. 569, 113–140.CrossRefGoogle Scholar
Wu, G.X. 1998 Wave radiation and diffraction by a submerged sphere in a channel. Q. J. Mech. Appl. Maths 51, 647–666.CrossRefGoogle Scholar
Yeung, R.W. & Sphaier, S.H. 1989 Wave-interference effects on a truncated cylinder in a channel. J. Engng Maths 23, 95–117.CrossRefGoogle Scholar