Skip to main content
SpringerLink
Log in

Flexural gravity wave scattering by a nearly vertical porous wall

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

Two-dimensional linear flexural gravity wave scattering by a nearly vertical porous wall is analyzed through a simplified perturbational analysis. A continuous semi-infinite ice sheet of uniform thickness is assumed to be floating over water of infinite depth. The ice sheet, with inclusion or exclusion of compressive stress, has either a free edge or a clamped edge at the porous wall. The first-order correction to the reflected flexural gravity wave amplitude is obtained by two different methods. The first method involves an application of Green’s theorem, and the second method involves a first kind integral equation. The integral equation method proves to be robust as it provides a complete solution in all cases of the problem, whereas the first method fails to produce the same when the ice sheet with a free edge is under compressive stress. The strain in the ice sheet and shear force along the ice sheet are computed and explained graphically for suitable parameters and a particular wall shape function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Stoker J (1957) Water waves. Interscience Publishers Inc., New York

    MATH  Google Scholar 

  2. Chakrabarti A (1992) Obliquely incident water waves against a vertical cliff. Appl Math Lett 5:13–17

    Article  MATH  Google Scholar 

  3. Mandal BN, Kar SK (1992) Reflection of water waves by a nearly vertical wall. Int J Math Educ Sci Technol 23(5):665–670

    Article  MATH  Google Scholar 

  4. Chakrabarti A, Sahoo T (1996) Reflection of water waves by a nearly vertical porous wall. J Austral Math Soc 37:417–429

    Article  MATH  MathSciNet  Google Scholar 

  5. Watanabe E, Utsunomiya T, Wang CM (2004) Hydroelastic analysis of pontoon-type VLFS: a literature survey. Eng Struct 26(2):245–256

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  8. Chakrabarti A, Ahluwalia DS, Manam SR (2003) Surface water waves involving a vertical barrier in the presence of an ice-cover. Int J Eng Sci 41:1145–1162

    Article  MATH  MathSciNet  Google Scholar 

  9. Williams TD, Squire VA (2002) Ice coupled waves near a deep water tide crack or ice jetty. In: Ice in the environment. Proceedings of the 16th IAHR international symposium on ice, Dunedin, New Zealand

  10. Brocklehurst P, Korobkin AA, Parau EI (2010) Interaction of hydro-elastic waves with a vertical wall. J Eng Math 68:215–231

    Article  MATH  MathSciNet  Google Scholar 

  11. Bhattacharjee J, Soares CG (2012) Flexural gravity wave over a floating ice sheet near a vertical wall. J Eng Math 75:29–48

    Article  MATH  Google Scholar 

  12. Manam SR, Bhattacharjee J, Sahoo T (2006) Expansion formulae in wave structure interaction problems. Proc R Soc Lond A 462:263–287

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. Yu X, Chwang AT (1994) Wave induced oscillation in harbour with porous breakwaters. J Waterw Port Coast Ocean Eng ASCE 120(2):125–144

    Article  Google Scholar 

  14. Yip TL, Sahoo T, Chwang AT (2001) Wave oscillation in a circular harbor with porous wall. J Appl Mech 68:603–607

    Article  MATH  Google Scholar 

  15. Manam SR, Kaligatla RB (2013) Structure-coupled gravity waves past a vertical porous barrier. J Eng Marit Environ 227(3):266–283

    Google Scholar 

  16. Manam SR, Kaligatla RB (2011) Effect of a submerged vertical barrier on flexural gravity waves. Int J Eng Sci 49:755–767

    Article  MATH  MathSciNet  Google Scholar 

  17. Sollitt CK, Cross RH (1972) Wave transmission through permeable breakwaters. In: Proceedings of the 13th conference on coastal engineering vancouver, Canada, pp 1827–1846

  18. Shaw DC (1985) Perturbational results for diffraction of water-waves by nearly-vertical barriers. IMA J Appl Math 34(1):99–117

    Article  MATH  MathSciNet  Google Scholar 

  19. Timoshenko S, Woinowsky-Krieger S (1970) Theory of plates and shells, 2nd edn. McGraw-Hill, Singapore

    Google Scholar 

  20. Evans DV (1976) A note on the waves produced by the small oscillations of a partially immersed vertical plate. J Inst Math Appl 17:135–140

    Article  MATH  Google Scholar 

  21. Karmakar D, Bhattacharjee J, Sahoo T (2007) Expansion formulae for wave structure interaction problems with applications in htdroelasticity. Int J Eng Sci 45:807–828

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  23. Schulkes RMSM, Hosking RJ, Sneyd AD (1987) Waves due to a steadily moving source on a floating ice plate. Part 2. J Fluid Mech 180:297–318

    Article  ADS  MATH  Google Scholar 

  24. Ugural A (1981) Stresses in plates and shells. McGraw Hill Book Company, New York

    Google Scholar 

  25. Squire VA (1993) The break up of shore fast sea ice. Cold Reg Sci Technol 21:211–218

    Article  Google Scholar 

  26. Squire VA, Martin S (1980) A field study of the physical properties, response to swell, and subsequent fracture of a single ice floe in the winter bering sea. Technical report 18, University of Washington

Download references

Acknowledgments

The authors are grateful to the referees for their valuable comments and suggestions which improved the presentation of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    R. B. Kaligatla & S. R. Manam

Authors
  1. R. B. Kaligatla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. R. Manam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. R. Manam.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaligatla, R.B., Manam, S.R. Flexural gravity wave scattering by a nearly vertical porous wall. J Eng Math 88, 49–66 (2014). https://doi.org/10.1007/s10665-014-9692-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10665-014-9692-7

Keywords

Search

Navigation