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Evaluation of exciting force and moment by a vertical floating cylinder in appearance of a coaxial cylindrical obstacle in two-layer fluid

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Abstract

In this work, we take into consideration a two-layer fluid system made up of a cylindrical buoy which is floating vertically in the upper fluid layer and a coaxial bottom-mounted cylindrical caisson placed in the bottom fluid layer. The analytical solution for the water wave diffraction caused by the proposed device has obtained by using the separation of variable method. In order to evaluate the undetermined coefficients to the diffracted velocity potential, we use matched eigenfunction expansion method. In two-layer flow, the incident wave propagates in two modes, namely mode of surface and internal-wave, and the hydrodynamic force occurs in both modes of motion. Further, we obtain hydrodynamic forces, namely, exciting force and moment acting on the device in each wave-mode of motion. We present the results of surge exciting force, heave exciting force and moment by the cylinders in surface and internal wave modes of motion along with various parameters of the device in wide range of frequencies. The significant effect of depth and draft ratios on the exciting forces and moments are observed in both modes of motion. The influence of surge and heave exciting forces by the lower cylinder exhibit almost similar trends and oscillations can be observed in moment for the surface wave mode. The obtained results are compared with the available established results. It can be seen that the results of the present work are in good agreement with established results. It validates the present results

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References

  1. Dean WR (1948) On the reflection of surface waves by a submerged circular cylinder. Proc Camb Philos Soc 44:483–491

    Article  MATH  Google Scholar 

  2. Black JL, Mei CC, Bray MCG (1971) Radiation and scattering of water wave by rigid bodies. J Fluid Mech 46:151–164

    Article  MATH  Google Scholar 

  3. Mohapatra SC, Islam H, Soares CG (2020) Boussinesq model and CFD simulations of non-linear wave diffraction by a floating vertical cylinder. J Mar Sci Eng 8(8):575

    Article  Google Scholar 

  4. Yeung RW (1981) Added mass and damping of a vertical cylinder in finite-depth waters. Appl Ocean Res 3:119–133

    Article  Google Scholar 

  5. Meylan MH, Taylor RE (2009) Time-dependent water-wave scattering by arrays of cylinders and the approximation of near trapping. J Fluid Mech 631:103–125

    Article  MathSciNet  MATH  Google Scholar 

  6. Zheng S, Zhang Y, Liu J, Gregorio I (2020) Wave diffraction from multiple truncated cylinders of arbitrary cross sections. Appl Math Model 77(2):1425–1445

    Article  MathSciNet  MATH  Google Scholar 

  7. Rahman M (1995) Water waves: Relating Modern Theory to Advanced Engineering Application. Applied Ocean Research. Clarendon Press, Oxford

    MATH  Google Scholar 

  8. Lee HS, Williams AN, Lee BH, Oh J (2002) Diffraction of multidirectional random waves by multiple rectangular submarine pits. Ocean Eng 30:85–106

    Google Scholar 

  9. Bhatta DD, Rahman M (2003) On scattering and Radiation problem for a cylinder in water of finite depth. Int J Eng Sci 41(9):931–967

    Article  MathSciNet  MATH  Google Scholar 

  10. Zheng YH, You YG, Shen YM (2004) On the radiation and diffraction of water waves by a rectangular buoy. Ocean Eng 31:1063–1082

    Article  Google Scholar 

  11. Wu B-J, Zheng Y-H, You Y-G (2006) Response amplitude and hydrodynamic force for a buoy over a convex. J Waterway Port Coast Ocean Eng 132(2):97–105

    Article  Google Scholar 

  12. Williams AN, Lee HS, Huang Z (2007) Floating pontoon breakwaters. Ocean Eng 27:221–240

    Article  Google Scholar 

  13. Lian Ji-Jian, Tong-Shun YU, Zhang Jin-Feng (2016) Wave force on composite bucket foundation of an offshore wind turbine. J Hydrodyn Ser B 28(1):33–42

    Article  Google Scholar 

  14. Wang P, Zhao M, Xiuli DU (2018) Short-crested, cnoidal, and solitary wave forces on composite bucket foundation for an offshore wind turbine. J Renew Sustain Energy 10:023305

    Article  Google Scholar 

  15. Wang P, Zhao M, Xiuli DU (2019) Short-crested wave-current forces on composite bucket foundation for an offshore wind turbine. Math Probl Eng, 1–9

  16. Michele S, Zheng S, Greaves D (2022) Wave energy extraction from a floating flexible circular plate. Ocean Eng 245:110275

    Article  Google Scholar 

  17. Behera H, Gayathri R, Selvan SA (2020) Wave attenuation by multiple outer porous barriers in the presence of an inner rigid cylinder. J Waterway Port Coast Ocean Eng 146(1):04019035

    Article  Google Scholar 

  18. Gayathri R, Behera H (2020) Mitigation of wave force on a circular flexible plate by a surface-piercing flexible porous barrier. Proc Inst Mech Eng Part M J Eng for the Marit Environ 235(2):586–599

    Google Scholar 

  19. Baines PG (1995) Topographic effects in stratified flows. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  20. Linton CM, McIver P (1995) The interaction of waves with horizontal cylinder in a two-layer fluid. J Fluid Mech 304:213–229

    Article  MathSciNet  MATH  Google Scholar 

  21. Sturova Izolia V (1999) Problems of radiation and diffraction for a circular cylinder in a stratified fluid. Fluid Dyn 34(4):521–533

    MATH  Google Scholar 

  22. Cadby JR, Linton CM (2000) Three-dimensional water-wave scattering in two-layer fluids. J Fluid Mech 423:155–173

    Article  MathSciNet  MATH  Google Scholar 

  23. Sherief HH, Faltas MS, Saad EI (2003) Forced gravity waves in two-layered fluids with the upper fluid having a free surface. Can J Phys 81(4):675–689

    Article  Google Scholar 

  24. Manam SR, Sahoo T (2005) Waves past porous structures in a two-layer fluid. J Eng Math 52:355–377

    Article  MathSciNet  MATH  Google Scholar 

  25. You Y-X, Shi-Qiang, Miao G-P (2007) The radiation and diffraction of water waves by a bottom-mounted circular cylinder in a two-layer fluid. J Hydrodyn Ser B 19(1):1–8

    Article  Google Scholar 

  26. Porter R, Zheng S, Liang H (2022) Scattering of surface waves by a vertical truncated structured cylinder. Proc R Soc A 478:20210824

    Article  MathSciNet  Google Scholar 

  27. Selvan SA, Gayathri R, Behera H, Melan MH (2021) Surface wave scattering by multiple flexible fishing cage system. Phys Fluids 33(3):037119-1–17

    Article  Google Scholar 

  28. Shi-Qiang, Yun-Xiang Y, Guc-Ping M (2008) Diffraction of water waves by a vertically floating cylinder in a two-layer fluid. China Ocean Eng 22(2):181–193

    Google Scholar 

  29. Xu F, Lu DQ (2010) Wave scattering by a thin elastic plate floating on a two-layer fluid. Int J Eng Sci 48:809–819

    Article  MathSciNet  MATH  Google Scholar 

  30. Mondal R, Sahoo T (2012) Wave structure interaction problems for two-layer fluids in three dimensions. Wave Motion 49:501–524

    Article  MathSciNet  MATH  Google Scholar 

  31. Behera H, Chiu-on NG, Sahoo T (2018) Oblique wave scattering by a floating elastic plate over a porous bed in single and two-layer fluid systems. Ocean Eng 159:280–294

    Article  Google Scholar 

  32. Selvan SA, Behera H (2020) Wave energy dissipation by a floating circular flexible porous membrane in single and two-layer fluids. Ocean Eng 206:107374-1–21

    Article  Google Scholar 

  33. Meylan MH, Bennetts LG, Peter MA (2016) Water wave scattering and energy dissipation by a floating porous elastic plate in three dimensions. Wave Motion 70:240–250

    Article  MathSciNet  MATH  Google Scholar 

  34. Mohapatra SC, Sahoo T (2014) Forced capillary-gravity wave motion of two-layer fluid in three-dimensions. Meccanica 49:939–960

    Article  MathSciNet  MATH  Google Scholar 

  35. Mohapatra SC, Karmakar D, Sahoo T (2011) On capillary gravity-wave motion in two-layer fluids. J Eng Math 71:253–277

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The research scholar shows his gratefulness to North Eastern Regional Institute of Science and Technology, Itanagar for giving GATE fellowship to carry out his research work. The authors would like to express their gratitude to the esteemed Reviewers for their insightful comments, from which the manuscript has been greatly improved. The authors are also highly indebted to the esteemed Editor Alexander Korobkin for giving a chance to revise their paper.

Funding

This work was supported by MHRD as the researcher C. K. Neog received MHRD Institute GATE scholarship from Govt. of India.

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Authors and Affiliations

  1. Department of Mathematics, North Eastern Regional Institute of Science and Technology, Itanagar, Arunachal Pradesh, 791 109, India

    Champak Kr. Neog & Mohammad Hassan

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  1. Champak Kr. Neog
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  2. Mohammad Hassan
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Contributions

All authors contributed to the study conception and design. Material preparation and analysis were performed by both authors. The first draft of the manuscript was written by C. K. Neog and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Mohammad Hassan.

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Neog, C.K., Hassan, M. Evaluation of exciting force and moment by a vertical floating cylinder in appearance of a coaxial cylindrical obstacle in two-layer fluid. J Eng Math 141, 5 (2023). https://doi.org/10.1007/s10665-023-10280-9

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  • DOI: https://doi.org/10.1007/s10665-023-10280-9

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