- Physical Review Journals
All JournalsPhysics Magazine

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

Wave interaction with a large number of ice floes of arbitrary shapes

Yifeng Yang and Guoxiong Wu*

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

Phys. Rev. Fluids 10, 124804 – Published 12 December, 2025

DOI: https://doi.org/10.1103/2r3s-16y4

Abstract

Water wave interaction with a large number of floes is investigated, based on the linearized velocity potential theory for fluid flow, and elastic thin plate theory for ice floes. The solution procedure starts from a domain decomposition approach, and equations for velocity potentials are constructed via the boundary integral method in the free-surface and ice-covered subdomains, separately. The velocity potentials and normal velocities at the interface of different domains are expressed in terms of eigenfunction expansions in the vertical direction. This allows the three-dimensional equation to be reduced to a set of two-dimensional ones. Continuity of velocity and pressure are then imposed at the interface. A formula for evaluating hydrodynamic forces is derived, which requires only the results on the floe edge. When the number of ice floes becomes large, an efficient scheme is introduced to reduce computational effort, while the desired accuracy is maintained. The procedure is applicable to ice floes of arbitrary shapes and arrangements. Case studies are conducted for single and double arrays of circular and elliptical ice floes. Extensive results are provided for the hydrodynamic forces and far-field scattered wave energy. Their features and corresponding physics are discussed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. D. Dumont, Marginal ice zone dynamics: History, definitions and research perspectives, Philos. Trans. R. Soc. A 380, 20210253 (2022).
  2. L. C. Smith and S. R. Stephenson, New trans-arctic shipping routes navigable by midcentury, Proc. Natl. Acad. Sci. USA 110, E1191 (2013).
  3. M. Ewing and A. P. Crary, Propagation of elastic waves in ice, part II, Physics 5, 181 (1934).
  4. M. H. Meylan and V. A. Squire, Response of a circular ice floe to ocean waves, J. Geophys. Res. 101, 8869 (1996).
  5. M. A. Peter, M. H. Meylan, and H. Chung, Wave scattering by a circular elastic plate in water of finite depth: A closed form solution, Int. J. Offshore Polar Eng. 14, 02 (2004).
  6. F. Montiel, L. G. Bennetts, V. A. Squire, F. Bonnefoy, and P. Ferrant, Hydroelastic response of floating elastic discs to regular waves. Part 2. Modal analysis, J. Fluid Mech. 723, 629 (2013).
  7. M. H. Meylan and L. G. Bennetts, Three-dimensional time-domain scattering of waves in the marginal ice zone, Philos. Trans. R. Soc. A 376, 20170334 (2018).
  8. R. Porter, The coupling between ocean waves and rectangular ice sheets, J. Fluids Struct. 84, 171 (2019).
  9. K. Ren, G. X. Wu, and Y. F. Yang, Surface wave interaction with floating elastic plates in channels, Phys. Fluids 36, 017143 (2024).
  10. M. H. Meylan, Wave response of an ice floe of arbitrary geometry, J. Geophys. Res. 107, 5 (2002).
  11. J. V. Wehausen and E. V. Laitone, Fluid Dynamics/Strömungsmechanik (Springer, Berlin, 1960), p. 446.
  12. C. D. Wang and M. H. Meylan, A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate, J. Fluids Struct. 19, 557 (2004).
  13. L. G. Bennetts and T. D. Williams, Wave scattering by ice floes and polynyas of arbitrary shape, J. Fluid Mech. 662, 5 (2010).
  14. M. A. Peter and M. H. Meylan, Infinite-depth interaction theory for arbitrary floating bodies applied to wave forcing of ice floes, J. Fluid Mech. 500, 145 (2004).
  15. L. G. Bennetts and V. A. Squire, Wave scattering by multiple rows of circular ice floes, J. Fluid Mech. 639, 213 (2009).
  16. F. Montiel, V. Squire, and L. Bennetts, Attenuation and directional spreading of ocean wave spectra in the marginal ice zone, J. Fluid Mech. 790, 492 (2016).
  17. Y. Y. Shi, Z. F. Li, and G. X. Wu, Interaction of wave with multiple wide polynyas, Phys. Fluids 31, 067111 (2019).
  18. F. Montiel, M. Meylan, and S. Hawkins, Scattering kernel of an array of floating ice floes: Application to water wave transport in the marginal ice zone, Proc. R. Soc. A 480, 20230633 (2024).
  19. J. Song, C.-C. Lu, and W. C. Chew, Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects, IEEE Trans. Antennas Propag. 45, 1488 (1997).
  20. V. A. Squire, Ocean wave interactions with sea ice: A reappraisal, Annu. Rev. Fluid Mech. 52, 37 (2020).
  21. C. Fox and V. A. Squire, On the oblique reflexion and transmission of ocean waves at shore fast sea ice, Philos. Trans. R. Soc. London Ser. A 347, 185 (1994).
  22. Y. Yang, G. Wu, and K. Ren, Hydroelastic wave interaction with a circular crack of an ice-cover in a channel, J. Fluids Struct. 130, 104173 (2024).
  23. 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).
  24. 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).
  25. 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).
  26. J. V. Wehausen, The wave resistance of ships, Adv. Appl. Mech. 13, 93 (1973).
  27. C. M. Linton and P. McIver, Handbook of Mathematical Techniques for Wave/Structure Interactions (CRC Press, Boca Raton, FL, 2001).
  28. Y. F. Yang, G. X. Wu, and K. Ren, Hydroelastic wave diffraction by a vertical circular cylinder standing in a channel with an ice cover, J. Fluid Mech. 941, A13 (2022).
  29. C. H. Lu, Y. S. He, and G. X. Wu, Coupled analysis of nonlinear interaction between fluid and structure during impact, J. Fluids Struct. 14, 127 (2000).
  30. M. N. Özişik, H. R. Orlande, M. J. Colaço, and R. M. Cotta, Finite Difference Methods in Heat Transfer (CRC Press, Boca Raton, FL, 2017).
  31. M. Abramowitz and I. A. Stegun, National Bureau of Standards Applied Mathematics 55 (U.S. Department of Commerce, 1965).
  32. Z. F. Li, G. X. Wu, and Y. Y. Shi, Wave diffraction by a circular crack in an ice sheet floating on water of finite depth, Phys. Fluids 30, 117103 (2018).
  33. K. E. Atkinson, An Introduction to Numerical Analysis (John Wiley & Sons, New York, 2008).
  34. 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).
  35. C. M. Linton, D. V. Evans, and F. T. Smith, The radiation and scattering of surface waves by a vertical circular cylinder in a channel, Philos. Trans. R. Soc. London Ser. A 338, 325 (1992).
  36. G. X. Wu, Wave radiation and diffraction by a submerged sphere in a channel, Q. J. Mech. Appl. Math. 51, 647 (1998).
  37. Y. F. Yang, G. X. Wu, and K. Ren, Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel, J. Fluid Mech. 928, A4 (2021).
  38. H. Liang, R. Porter, and S. M. Zheng, Wave scattering by plate array metacylinders of arbitrary cross-section, J. Fluid Mech. 1001, A6 (2024).
  39. H. Maniar and J. Newman, Wave diffraction by a long array of cylinders, J. Fluid Mech. 339, 309 (1997).

Outline

Information

Phys. Rev. Fluids 10, 124804– Published 12 December, 2025
  • Received 7 September 2025
  • Accepted 14 November 2025
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