- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Wave motions due to a point source pulsating and advancing at forward speed parallel to a semi-infinite ice sheet

Z. F. Li1, G. X. Wu2,*, and Y. Y. Shi1

  • 1School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
  • 2Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom

  • *Corresponding author: g.wu@ucl.ac.uk
PDF

Phys. Rev. Fluids 9, 014801 – Published 5 January, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.014801

Abstract

The Green function, or the wave motion due to a point source pulsating and advancing at constant forward speed along a semi-infinite ice sheet in finite water depth is investigated, based on the linear velocity potential theory for fluid flow and thin elastic plate model for the ice sheet. The result is highly relevant to the ship motions near marginal seas. The ice edge is assumed to be free, or zero bending moment and shear-force conditions are used, while other edge conditions can be similarly considered. The Green function G is derived first through the Fourier transform along the direction of forward speed and then by the Wiener-Hopf technique along the transverse direction across both the free surface and ice sheet. The result shows that in the ice-covered domain, G can be decomposed into three parts. The first one is that upper ocean surface is fully covered by an ice sheet, and the second and third ones are due to the free surface and ice edge. Similarly, in the free-surface domain, G contains the component corresponding to that the upper water surface is fully free, while the second and third ones are due to the ice sheet and ice edge. In both domains, the latter two are due to the interactions of the free-surface wave and ice sheet deflection, which leads to the major complication. In-depth investigations are made for each part of G, and aim to shed some light on the nature of the wave motions induced by a ship advancing along a semi-infinite ice sheet at constant forward speed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. M. Casas-Prat and X. L. Wang, Projections of extreme ocean waves in the Arctic and potential implications for coastal inundation and erosion, J. Geophys. Res.: Oceans 125, e2019JC015745 (2020).
  2. Y. Aksenov, E. E. Popova, A. Yool, A. J. G. Nurser, T. D. Williams, L. Bertino, and J. Bergh, On the future navigability of Arctic sea routes: High-resolution projections of the Arctic Ocean and sea ice, Mar. Policy 75, 300 (2017).
  3. G. Q. Robin, Wave propagation through fields of pack ice, Philos. Trans. R. Soc. A255, 313 (1963).
  4. V. A. Squire, Ocean wave interactions with sea ice: A reappraisal, Annu. Rev. Fluid Mech. 52, 37 (2020).
  5. J. V. Wehausen and E. V. Laitone, Surface Waves, Handbuch des Physik (Springer Verlag, Berlin, 1960).
  6. P. A. Milewski, J. M. Vanden-Broeck, and Z. Wang, Hydroelastic solitary waves in deep water, J. Fluid Mech. 679, 628 (2011).
  7. C. Fox and V. A. Squire, Reflection and transmission characteristics at the edge of shore fast sea ice, J. Geophys. Res.: Oceans 95, 11629 (1990).
  8. C. Fox and V. A. Squire, Strain in shore fast ice due to incoming ocean waves and swell, J. Geophys. Res.: Oceans 96, 4531 (1991).
  9. C. Fox and V. A. Squire, On the oblique reflexion and transmission of ocean waves at shore fast sea ice, Philos. Trans. R. Soc. A347, 185 (1994).
  10. T. Sahoo, T. L. Yip, and A. T. Chwang, Scattering of surface waves by a semi-infinite floating elastic plate, Phys. Fluids 13, 3215 (2001).
  11. A. Chakrabarti, On the solution of the problem of scattering of surface–water waves by the edge of an ice cover, Proc. R. Soc. London A 456, 1087 (2000).
  12. N. J. Balmforth and R. V. Craster, Ocean waves and ice sheets, J. Fluid Mech. 395, 89 (1999).
  13. L. A. Tkacheva, The diffraction of surface waves by a floating elastic plate at oblique incidence, J. Appl. Math. Mech. 68, 425 (2004).
  14. C. M. Linton and H. Chung, Reflection and transmission at the ocean/sea-ice boundary, Wave Motion 38, 43 (2003).
  15. K. Eliasson, G. F. Ulfarsson, T. Valsson, and S. M. Gardarsson, Identification of development areas in a warming Arctic with respect to natural resources, transportation, protected areas, and geography, Futures 85, 14 (2017).
  16. I. V. Sturova, Radiation of waves by a cylinder submerged in water with ice floe or polynya, J. Fluid Mech. 784, 373 (2015).
  17. I. V. Sturova and L. A. Tkacheva, Wave radiation by a cylinder submerged in water with an ice floe or a polynya, in The 30th International Workshop on Water Waves and Floating Bodies (IWWWFB, Bristol, UK, 2015).
  18. K. Ren, G. X. Wu, and G. A. Thomas, Wave excited motion of a body floating on water confined between two semi-infinite ice sheets, Phys. Fluids 28, 127101 (2016).
  19. Z. F. Li, Y. Y. Shi, and G. X. Wu, Interaction of waves with a body floating on polynya between two semi-infinite ice sheets, J. Fluids Struct. 78, 86 (2018).
  20. Z. F. Li, Y. Y. Shi, and G. X. Wu, Interaction of wave with a body floating on a wide polynya, Phys. Fluids 29, 097104 (2017).
  21. K. Ren, G. X. Wu, and C. Y. Ji, Wave diffraction and radiation by a vertical circular cylinder standing in a three-dimensional polynya, J. Fluids Struct. 82, 287 (2018).
  22. Z. F. Li, Y. Y. Shi, and G. X. Wu, A hybrid method for linearized wave radiation and diffraction problem by a three dimensional floating structure in a polynya, J. Comput. Phys. 412, 109445 (2020).
  23. Z. F. Li, G. X. Wu, and K. Ren, Interactions of waves with a body floating in an open water channel confined by two semi-infinite ice sheets, J. Fluid Mech. 917, A19 (2021).
  24. Z. F. Li and G. X. Wu, Hydrodynamic force on a ship floating on the water surface near a semi-infinite ice sheet, Phys. Fluids 33, 127101 (2021).
  25. H. Liang and X. B. Chen, Asymptotic analysis of capillary–gravity waves generated by a moving disturbance, Eur. J. Mech. B Fluids 72, 624 (2018).
  26. M. Rabaud and F. Moisy, Ship wakes: Kelvin or Mach angle? Phys. Rev. Lett. 110, 214503 (2013).
  27. A. Darmon, M. Benzaquen, and E. Raphaël, Kelvin wake pattern at large Froude numbers, J. Fluid Mech. 738, R3 (2014).
  28. J. W. Davys, R. J. Hosking, and A. D. Sneyd, Waves due to a steadily moving source on a floating ice plate, J. Fluid Mech. 158, 269 (1985).
  29. T. Takizawa, Deflection of a floating sea ice sheet induced by a moving load, Cold Reg. Sci. Technol. 11, 171 (1985).
  30. F. Milinazzo, M. Shinbrot, and N. W. Evans, A mathematical analysis of the steady response of floating ice to the uniform motion of a rectangular load, J. Fluid Mech. 287, 173 (1995).
  31. K. A. Shishmarev, T. I. Khabakhpasheva, and A. A. Korobkin, The ice response to an oscillating load moving along a frozen channel, IOP Conf. Ser.: Earth Environ. Sci. 193, 012072 (2018).
  32. L. A. Tkacheva, Behavior of a semi-infinite ice cover under a uniformly moving load, J. Appl. Mech. Tech. Phys. 59, 258 (2018).
  33. L. A. Tkacheva, Wave motion in an ice sheet with crack under uniformly moving load, Fluid Dyn. 54, 14 (2019).
  34. I. V. Sturova and L. A. Tkacheva, Movement of external load over free surface of fluid in the ice channel, J. Phys. Conf. Ser. 1268, 012066 (2019).
  35. S. P. Timoshenko and K. S. Woinowsky, Theory of Plates and Shells (McGraw-Hill, Singapore, 1959).
  36. J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1978).
  37. B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London, 1958).
  38. X. B. Chen and G. X. Wu, On singular and highly oscillatory properties of the Green function for ship motions, J. Fluid Mech. 445, 77 (2001).
  39. H. Liang and X. B. Chen, Viscous effects on the fundamental solution to ship waves, J. Fluid Mech. 879, 744 (2019).
  40. V. A. Squire, J. P. Dugan, P. Wadhams, P. J. Rottier, and A. K. Liu, Of ocean waves and sea ice, Annu Rev Fluid Mech 27, 115 (1995).
  41. O. M. Faltinsen, Hydrodynamics of High-Speed Marine Vehicles (Cambridge University Press, New York, 2005).
  42. J. Thomson, Y. L. Fan, S. Stammerjohn, J. Stopa, W. E. Rogers, F. Girard-Ardhuin, F. Ardhuin, H. L. Shen, W. Perrie, H. Shen et al., Emerging trends in the sea state of the Beaufort and Chukchi seas, Ocean Modell. 105, 1 (2016).
  43. D. V. Evans and R. Porter, Wave scattering by narrow cracks in ice sheets floating on water of finite depth, J. Fluid Mech. 484, 143 (2003).
  44. P. Brocklehurst, A. A. Korobkin, and E. I. Părău, Interaction of hydro-elastic waves with a vertical wall, J. Eng. Math. 68, 215 (2010).
  45. A. A. Korobkin, S. Malenica, and T. Khabakhpasheva, Interaction of flexural-gravity waves in ice cover with vertical walls, Philos. Trans. R. Soc. A376, 20170347 (2018).
  46. X. B. Chen, Peculiar properties of ship-motion Green functions in water of finite depth, in The 15th International Workshop on Water Waves and Floating Bodies (IWWWFB, Caesarea, Israel, 2000).
  47. G. X. Wu, Radiation and diffraction by a submerged sphere advancing in water waves of finite depth, Proc. R. Soc. London A 448, 29 (1995).
  48. X. B. Chen and F. Noblesse, Dispersion relation and far-field waves, in The 12th International Workshop on Water Waves and Floating Bodies (IWWWFB, Marseille, France, 1997).
  49. F. Noblesse and X. B. Chen, Decomposition of free-surface effects into wave and near-field components, Ship Technol. Res. 42, 167 (1995).

Outline

Information

Phys. Rev. Fluids 9, 014801– Published 5 January, 2024
  • Received 15 May 2023
  • Accepted 31 October 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation