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A boundary-integral method for the interaction of large-amplitude ocean waves with a compliant floating raft such as a sea-ice floe

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Abstract

The interaction of large-amplitude water waves with a compliant floating raft such as a sea-ice floe or a pontoon-type VLFS (very large floating structure) is considered. The solution is expressed as a series using a perturbation expansion, the first two components of which are solved inductively using a boundary-integral method. The primary interest of this paper is to the ways in which the second-order potential can be modified in order to apply the boundary-integral method and to the comparison of results with those derived using eigenfunction matching methods.

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References

  1. Squire VA (2007) Of ocean waves and sea-ice revisited. Cold Reg Sci Technol 49(2): 110–133

    Article  Google Scholar 

  2. Balmforth NJ, Craster RV (1999) Ocean waves and ice sheets. J Fluid Mech 395: 89–124

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. Chakrabarti A (2000) On the solution of the problem of scattering of surface-water waves by the edge of an ice cover. Proc R Soc Lon Ser-A 456(1997): 1087–1099

    Article  MATH  ADS  Google Scholar 

  4. Squire VA, Dixon TW (2000) An analytic model for wave propagation across a crack in an ice sheet. Int J Offshore Polar 10(3): 173–176

    Google Scholar 

  5. Squire VA, Dixon TW (2001) How a region of cracked sea ice affects ice-coupled wave propagation. Ann Glaciol 33: 327–332

    Article  ADS  Google Scholar 

  6. Squire VA, Dixon TW (2001) On modelling an iceberg embedded in shore fast sea ice. J Eng Math 40(3): 211–236

    Article  MATH  MathSciNet  Google Scholar 

  7. Sahoo T, Yip TL, Chwang AT (2001) Scattering of surface waves by a semi-infinite floating elastic plate. Phys Fluids 13(11): 3215–3222

    Article  ADS  Google Scholar 

  8. Linton CM, Chung H (2003) Reflection and transmission at the ocean/sea-ice boundary. Wave Motion 38(1): 43–52

    Article  MATH  MathSciNet  Google Scholar 

  9. Porter D, Porter R (2004) Approximations to wave scattering by an ice sheet of variable thickness over undulating bed topography. J Fluid Mech 509: 145–179

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Chung H, Linton CM (2005) Reflection and transmission of waves across a gap between two semi-infinite elastic plates on water. Q J Mech Appl Math 58(1): 1–15

    Article  MATH  MathSciNet  Google Scholar 

  11. Manam SR, Bhattacharjee J, Sahoo T (2006) Expansion formulae in wave structure interaction problems. Proc R Soc Lon Ser-A 462(2065): 263–287

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Bennetts LG, Biggs NRT, Porter D (2007) A multi-mode approximation to wave scattering by ice sheets of varying thickness. J Fluid Mech 579: 413–443

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Williams TD, Squire VA (2006) Scattering of flexural-gravity waves at the boundaries between three floating sheets with applications. J Fluid Mech 569: 113–140

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Williams TD, Squire VA (2007) Wave scattering at the sea-ice/ice-shelf transition with other applications. SIAM J Appl Math 67(4): 938–959

    Article  MATH  MathSciNet  Google Scholar 

  15. Squire VA, Dugan JP, Wadhams P, Rottier PJ, Liu AK (1995) Of ocean waves and sea ice. Annu Rev Fluid Mech 27: 115–168

    Article  ADS  MathSciNet  Google Scholar 

  16. Fox C (2002) Large amplitude sea/ice coupling. In: Murthy TKS, Sackinger WM, Wadhams P (eds) Advances in ice technology. Proc. 3rd Int. Conf. Ice Tech. Computational Mechanics Publications, Cambridge, MA, pp 291–304

  17. Hegarty GM, Squire VA (2002) Large amplitude periodic waves beneath an ice sheet. In: Squire VA, Langhorne PJ (eds) Ice in the environment. Proceedings of the 16th international symposium on ice, vol 2. International Association of Hydraulic Engineering and Research, University of Otago, Dunedin, NZ, pp 310–317

  18. Hegarty GM, Squire VA (2004) On modelling the interaction of large amplitude waves with a solitary floe. In: Chung JS, Izumiyama K, Sayed M, Hong SW (eds) Proceedings of the 14th international offshore and polar engineering conference, vol 1. International Society of Offshore and Polar Engineers, Cupertino, CA, pp 845–850

  19. Rothrock DA, Yu Y, Maykut GA (1999) Thinning of the Arctic sea-ice cover. Geophys Res Lett 26(23): 3469–3472

    Article  ADS  Google Scholar 

  20. Wadhams P, Davis NR (2000) Further evidence of ice thinning in the Arctic Ocean. Geophys Res Lett 27(24): 3973–3976

    Article  ADS  Google Scholar 

  21. Comiso J (2002) A rapidly declining perennial sea-ice cover in the Arctic. Geophys Res Lett 29(20):1956. doi:10.1029/2002GL015650

  22. Meylan MH, Squire VA (1994) The response of ice floes to ocean waves. J Geophys Res 99(C1): 899–900

    Article  Google Scholar 

  23. Eatock Taylor R (2007) Hydroelastic analysis of plates and some approximations. J Eng Math 58(1–4): 267–278

    Article  MATH  MathSciNet  Google Scholar 

  24. Verne J (1896) The floating island. Sampson Low, Marston and Co, London

    Google Scholar 

  25. Forbes LK (1986) Surface waves of large amplitude beneath an elastic sheet. Part 1. High-order series solution. J Fluid Mech 169: 409–428

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Forbes LK (1986) Surface waves of large amplitude beneath an elastic sheet. Part 2. Galerkin solution. J Fluid Mech 188: 491–508

    Article  ADS  MathSciNet  Google Scholar 

  27. Fung YC (1965) Foundations of solid mechanics. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  28. Washizu K (1982) Variational methods in elasticity and plasticity. Pergamon, New York

    MATH  Google Scholar 

  29. Drozdov AD (1996) Finite elasticity and viscoelasticity: a course in the nonlinear mechanics of solids. World Scientific, Singapore

    MATH  Google Scholar 

  30. Stoker JJ (1957) Water waves the mathematical theory with applications. Interscience, New York

    MATH  Google Scholar 

  31. Williams TD (2005) Reflections on ice: the scattering of flexural-gravity waves by irregularities in Arctic and Antarctic ice sheets. PhD thesis, University of Otago, Dunedin, NZ

  32. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Publications, New York

    Google Scholar 

  33. Weisstein EW (1999) CRC concise encyclopedia of mathematics. CRC Press, Boca Raton

    Google Scholar 

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Hegarty, G.M., Squire, V.A. A boundary-integral method for the interaction of large-amplitude ocean waves with a compliant floating raft such as a sea-ice floe. J Eng Math 62, 355–372 (2008). https://doi.org/10.1007/s10665-008-9219-1

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  • DOI: https://doi.org/10.1007/s10665-008-9219-1

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