Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T10:34:02.713Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

Published online by Cambridge University Press:  04 October 2021

Y.F. Yang ,
G.X. Wu Open the ORCID record for G.X. Wu [Opens in a new window]  and
K. Ren Open the ORCID record for K. Ren [Opens in a new window]
Y.F. Yang
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
G.X. Wu*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
K. Ren
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed.

JFM classification

Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Channel flow Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A4
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I.A. 1970 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, vol. 55. US Government Printing Office.Google Scholar
Balmforth, N.J. & Craster, R.V. 1999 Ocean waves and ice sheets. J. Fluid Mech. 395, 89–124.CrossRefGoogle 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
Brocklehurst, P., Korobkin, A.A. & Părău, E.I. 2011 Hydroelastic wave diffraction by a vertical cylinder. Phil. Trans. R. Soc. Lond. A 369 (1947), 2832–2851.Google ScholarPubMed
Das, D. & Mandal, B.N. 2008 Water wave radiation by a sphere submerged in water with an ice-cover. Arch. Appl. Mech. 78 (8), 649–661.CrossRefGoogle Scholar
Dişibüyük, N.B., Korobkin, A.A. & Yılmaz, O. 2020 Diffraction of flexural-gravity waves by a vertical cylinder of non-circular cross section. Appl. Ocean Res. 101, 102234.CrossRefGoogle Scholar
Evans, D.V. & Porter, R. 1997 Near-trapping of waves by circular arrays of vertical cylinders. Appl. Ocean Res. 19 (2), 83–99.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
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
Haussling, H.J. & Coleman, R.M. 1979 Nonlinear water waves generated by an accelerated circular cylinder. J. Fluid Mech. 92 (4), 767–781.CrossRefGoogle Scholar
Havelock, T.H. 1936 The forces on a circular cylinder submerged in a uniform stream. Proc. R. Soc. Lond. A 157 (892), 526–534.Google Scholar
Khabakhpasheva, T.I., Shishmarev, K. & Korobkin, A.A. 2019 Large-time response of ice cover to a load moving along a frozen channel. Appl. Ocean Res. 86, 154–165.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
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google 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., Wu, G. & Ren, K. 2021 Interactions of waves with a body floating in an open water channel confined by two semi-infinite ice sheets. J. Fluid Mech. 917, A19.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. 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. 1993 On the free-surface green's function for channel problems. Appl. Ocean Res. 15 (5), 263–267.CrossRefGoogle Scholar
Linton, C.M., Evans, D.V. & Smith, F.T. 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.CrossRefGoogle Scholar
Linton, C.M. & McIver, P. 2001 Handbook of Mathematical Techniques for Wave/Structure Interactions. CRC Press.CrossRefGoogle Scholar
Mei, C.C. & Chen, H.S. 1976 A hybrid element method for steady linearized free-surface flows. Intl J. Numer. Meth. Engng 10 (5), 1153–1175.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
Newman, J.N. 1969 Lateral motion of a slender body between two parallel walls. J. Fluid Mech. 39 (1), 97–115.CrossRefGoogle Scholar
Newman, J.N. 2017 Trapped-wave modes of bodies in channels. J. Fluid Mech. 812, 178–198.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. 2007 Diffraction of flexural waves by finite straight cracks in an elastic sheet over water. J. Fluids Struct. 23 (2), 309–327.CrossRefGoogle Scholar
Ren, K., Wu, G.X. & Ji, C.Y. 2018 a Diffraction of hydroelastic waves by multiple vertical circular cylinders. J. Engng Maths 113 (1), 45–64.CrossRefGoogle Scholar
Ren, K., Wu, G.X. & Ji, C.Y. 2018 b 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. & Li, Z.F. 2020 Hydroelastic waves propagating in an ice-covered channel. J. Fluid Mech. 886.CrossRefGoogle Scholar
Scullen, D & Tuck, E.O. 1995 Nonlinear free-surface flow computations for submerged cylinders. J. Ship Res. 39 (3), 185–193.Google Scholar
Semenov, Y.A. & Wu, G.X. 2020 Free-surface gravity flow due to a submerged body in uniform current. J. Fluid Mech. 883, A60.CrossRefGoogle Scholar
Shishmarev, K., Khabakhpasheva, T. & Korobkin, A.A. 2016 The response of ice cover to a load moving along a frozen channel. Appl. Ocean Res. 59, 313–326.CrossRefGoogle Scholar
Squire, V.A. 2007 Of ocean waves and sea-ice revisited. Cold Reg. Sci. Technol. 49 (2), 110–133.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
Timoshenko, S.P. & Woinowsky-Krieger, S. 1959 Theory of Plates and Shells. McGraw-Hill.Google Scholar
Tuck, E.O. 1965 The effect of non-linearity at the free surface on flow past a submerged cylinder. J. Fluid Mech. 22 (2), 401–414.CrossRefGoogle Scholar
Ursell, F. 1949 On the heaving motion of a circular cylinder on the surface of a fluid. Q. J. Mech. Appl. Maths 2 (2), 218–231.CrossRefGoogle Scholar
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged circular cylinder. I. Math. Proc. Camb. Phil. Soc. 46 (1), 141–152.CrossRefGoogle Scholar
Ursell, F. 1951 Trapping modes in the theory of surface waves. Math. Proc. Camb. Phil. Soc. 47, 347–358.CrossRefGoogle Scholar
Utsunomiya, T. & Eatock Taylor, R. 1999 Trapped modes around a row of circular cylinders in a channel. J. Fluid Mech. 386, 259–279.CrossRefGoogle Scholar
Wehausen, J.V. & Laitone, E.V. 1960 Surface waves. In Fluid Dynamics/Strömungsmechanik, pp. 446–778. Springer.CrossRefGoogle Scholar
Wu, G.X. 1995 Radiation and diffraction by a submerged sphere advancing in water waves of finite depth. Proc. R. Soc. Lond. A 448 (1932), 29–54.Google Scholar
Wu, G.X. 1998 a Wave radiation and diffraction by a submerged sphere in a channel. Q. J. Mech. Appl. Maths 51 (4), 647–666.CrossRefGoogle Scholar
Wu, G.X. 1998 b Wavemaking resistance on a submerged sphere in a channel. J. Ship Res. 42 (1), 1–8.CrossRefGoogle Scholar
Wu, G.X. & Eatock Taylor, R. 1987 Hydrodynamic forces on submerged oscillating cylinders at forward speed. Proc. R. Soc. Lond. A 414 (1846), 149–170.Google Scholar