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Scattering of oblique waves by a semi-infinite floating elastic plate within the framework of wave blocking

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Abstract

Scattering of obliquely incident surface gravity wave by a semi-infinite floating elastic plate in the presence of lateral compressive force is studied within the framework of blocking dynamics in time-space. In the presence of lateral compressive force, primary and secondary wave blocking occur for two different values of time-period where the group velocity vanishes, whilst the phase velocity remains positive. Moreover, for each time-period within the limits of blocking points, three propagating wave modes exist in the plate-covered region, out of which two are related with positive group velocities and another one is associated with the negative group velocity. Further, all the three wave modes coalesce at the saddle point for a particular value of the compressive force. The energy identity for the scattering problem in the case of multiple propagating modes depends on the amplitude of the reflected and transmitted waves as well as the ratio of the energy transfer rate. In the case of obliquely incident waves, full-wave reflection occurs beyond a critical angle for a certain time-period whilst the same phenomenon occurs for certain incident angles before a critical time-period. Moreover, the scattering coefficients are having removable singularities at the blocking as well as saddle points. Besides, irregular pattern in plate deflection occurs due to the superposition of multiple propagating wave modes for a certain time-period within the blocking limits. The normal strain in the floating plate sheet has a certain oscillatory pattern for the time-period lying within the limits of blocking points. Surface plots for the scattering coefficients as well as plate deflection are demonstrated for various values of incident angle as well as compressive force. A comparison of various results in the case of small amplitude wave theory and shallow water approximation reveals the accuracy of the analysis in different cases.

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References

  1. El-Shihy AA, Ezquiaga JM (2019) Architectural design concept and guidelines for floating structures for tackling sea level rise impacts on abu-qir. Alex Eng J 58(2):507–518

    Article  Google Scholar 

  2. Squire VA (2020) Ocean wave interactions with sea ice: a reappraisal. Annu Rev Fluid Mech 52:37–60

    Article  Google Scholar 

  3. Diffenbaugh NS, Singh D, Mankin JS, Horton DE, Swain DL, Touma D, Charland A, Liu Y, Haugen M, Tsiang M, Rajaratnam B (2017) Quantifying the influence of global warming on unprecedented extreme climate events. Proc Natl Acad Sci 114(19):4881–4886

    Article  Google Scholar 

  4. Durand G, van den Broeke MR, Cozannet GL, Edwards TL, Holland PR, Jourdain NC, Marzeion B, Mottram R, Nicholls RJ, Pattyn F, Paul F (2022) Sea-level rise: From global perspectives to local services. Front Mar Sci 2088

  5. Wang CM, Tay ZY (2011) Very large floating structures: applications, research and development. Procedia Eng 14:62–72

    Article  Google Scholar 

  6. Pardo ML, Iglesias G, Carral L (2015) A review of very large floating structures (VLFS) for coastal and offshore uses. Ocean Eng 109:677–690

    Article  Google Scholar 

  7. Ding J, Wu Y, Xie Z, Yang W, Wang S, Yu J, Yu T (2021) Overview: research on hydroelastic responses of VLFS in complex environments. Mar Struct 78:102978

    Article  Google Scholar 

  8. Nguyen HP, Wang CM, Tay ZY, Luong VH (2020) Wave energy converter and large floating platform integration: a review. Ocean Eng 213:107768

    Article  Google Scholar 

  9. Aryai V, Abbassi R, Abdussamie N, Salehi F, Garaniya V, Asadnia M, Baksh A-A, Penesis I, Karampour H, Draper S, Magee A (2021) Reliability of multi-purpose offshore-facilities: present status and future direction in Australia. Process Saf Environ Prot 148:437–461

    Article  Google Scholar 

  10. Li L, Ruzzo C, Collu M, Gao Y, Failla G, Arena F (2020) Analysis of the coupled dynamic response of an offshore floating multi-purpose platform for the blue economy. Ocean Eng 217:107943

    Article  Google Scholar 

  11. Squire VA (2008) Synergies between VLFS hydroelasticity and sea ice research. Int J Offshore Polar Eng 18(04)

  12. Greenhill AG (1886) Wave motion in hydrodynamics. Am J Math 9:62–96

    Article  MathSciNet  Google Scholar 

  13. Fox C, Squire VA (1994) On the oblique reflexion and transmission of ocean waves at shore fast sea ice. Philos Trans R. Soc A 347(1682):185–218

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. 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  Google Scholar 

  16. Tkacheva LA (2004) The diffraction of surface waves by a floating elastic plate at oblique incidence. J Appl Math Mech 68(3):425–436

    Article  Google Scholar 

  17. Karmakar D, Soares CG (2012) Scattering of gravity waves by a moored finite floating elastic plate. Appl Ocean Res 34:135–149

    Article  Google Scholar 

  18. Korobkin A, Părău EI, Broeck JMV (2011) The mathematical challenges and modelling of hydroelasticity. Philos Trans R Soc A 369(1947):2803–2812

    Article  MathSciNet  Google Scholar 

  19. Sahoo T (2012) Mathematical techniques for wave interaction with flexible structures. CRC Press, Boca Raton

    Book  Google Scholar 

  20. Guo Y, Liu Y, Meng X (2016) Oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography. Acta Oceanol Sin 35(7):113–121

    Article  Google Scholar 

  21. 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  Google Scholar 

  22. Bukatov AE, Zav’yalov DD (1995) Impingement of surface waves on the edge of compressed ice. Fluid Dyn 30(3):435–440

    Article  Google Scholar 

  23. Karmakar D, Bhattacharjee J, Sahoo T (2010) Oblique flexural gravity-wave scattering due to changes in bottom topography. J Eng Math 66(4):325–341

    Article  MathSciNet  Google Scholar 

  24. Das S, Sahoo T, Meylan MH (2018) Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity. Proc R Soc Lond Ser A 474(2209):20170223

    MATH  Google Scholar 

  25. Das S, Sahoo T, Meylan MH (2018) Flexural-gravity wave dynamics in two-layer fluid: blocking and dead water analogue. J Fluid Mech 854:121–145

    Article  MathSciNet  Google Scholar 

  26. Boral S, Nath S, Sahoo T, Meylan MH (2021) The role of viscoelastic foundation on flexural gravity wave blocking in shallow water. AIP Adv 11(6):065317

    Article  Google Scholar 

  27. Barman SC, Das S, Sahoo T, Meylan MH (2021) Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking. J Fluid Mech 916(A11)

  28. Boral S, Meylan MH, Sahoo T (2021) Time-dependent wave propagation on a variable Winkler foundation with compression. Wave Motion 106:102792

    Article  MathSciNet  Google Scholar 

  29. Barman SC, Boral S, Sahoo T, Meylan MH (2021) Bragg scattering of long flexural gravity waves by an array of submerged trenches and the analysis of blocking dynamics. AIP Adv 11(11):115308

    Article  Google Scholar 

  30. Dean RG, Dalrymple RA (1991) Water wave mechanics for engineers and scientists Advanced Series in Ocean Engineering, vol 2. World Scientific Publishing Company, Singapore

    Book  Google Scholar 

  31. Sturova IV (1999) Oblique incidence of surface waves on an elastic plate. J Appl Mech Tech Phys 40(4):604–610

    Article  Google Scholar 

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Acknowledgements

PN acknowledges the financial support received from the Department of Science and Technology, Government of India through award No: DST/CCP/CoE/79/2017(G). SB acknowledges the financial support received from the Council of Scientific and Industrial Research, New Delhi, India through the senior research fellowship vide file no: 09/081(1345)/2019-EMR-I.

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Negi, P., Boral, S. & Sahoo, T. Scattering of oblique waves by a semi-infinite floating elastic plate within the framework of wave blocking. J Eng Math 135, 1 (2022). https://doi.org/10.1007/s10665-022-10230-x

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