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Reduction of wave impact on seashore as well as seawall by floating structure and bottom topography

  • Amandeep Kaur
  • S. C. MarthaEmail author
Article
  • 14 Downloads

Abstract

The three-dimensional problem involving diffraction of water wave by a finite floating rigid dock over an arbitrary bottom is studied for two cases (i) in the absence of wall (ii) in the presence of wall. The problem is handled for its solution with the aid of step method. Here both asymmetric and symmetric arbitrary bottom profile is approximated using successive steps. Step approximation helps to apply the matched eigenfunction expansion method, in result, system of algebraic equations are obtained which are solved to determine the hydrodynamic quantities, namely, force experienced by rigid floating dock as well as rigid seawall, free surface elevation, transmission & reflection coefficients associated with transmission & reflected waves respectively. The effects of various structural and system parameters are examined on these hydrodynamics quantities. The appropriate values of length and thickness of dock, water depth and angle of incidence provide the salient information to marine and coastal engineers to design the offshore structures and creation of parabolic trench on the bottom. The present results are compared with known results for special case of bottom topography. The energy balance relation is derived and checked.

Key words

Arbitrary bottom step approximation hydrodynamic quantities 

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Notes

Acknowledgment

The authors thank the reviewers and associate editor of Journal of Hydrodynamics for their comments and suggestions to improve the article in the present form. A. Kaur thanks DST, India for support through inspire fellowship.

References

  1. [1]
    Linton C. M. The finite dock problem [J]. Zeitschrift fr angewandte Mathematik und Physik ZAMP, 2001, 52(4): 640–656.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Chakrabarti A., Mandal B. N., Gayen R. The Dock problem revisited [J]. International Journal of Mathematics and Mathematical Sciences, 2005, 21: 3459–3470.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Cho I. H., Kim M. H. Interactions of a horizontal flexible membrane with oblique incident waves [J]. Journal of Fluid Mechanics, 1998, 367: 139–161.CrossRefGoogle Scholar
  4. [4]
    Martha S. C., Bora S. N. Reflection and transmission coefficients for water wave scattering by a sea-bed with small undulation [J]. Journal of Applied Mathematics and Mechanics, 2007, 87(4): 314–321.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Xie J., Liu H. W. An exact analytic solution to the modified mild-slope equation for waves propagating over a trench with various shapes [J]. Ocean Engineering, 2012, 50: 72–82.CrossRefGoogle Scholar
  6. [6]
    Lin P., Liu H. W. Analytical study of linear-wave reflection by a two-dimensional obstacle of general trapezoidal shape [J]. Journal of Engineering Mechanics, 2005, 131: 822–830.CrossRefGoogle Scholar
  7. [7]
    Xie J. J., Liu H. W., Lin P. Analytical solution for long-wave reflection by a rectangular obstacle with two scour trenches [J]. Journal of Engineering Mechanics, 2011, 137(12): 919–930.CrossRefGoogle Scholar
  8. [8]
    Wang, C. D., Meylan M. H. The linear wave response of a floating thin plate on water of variable depth [J]. Applied Ocean Research, 2002, 24: 163–174.CrossRefGoogle Scholar
  9. [9]
    Xu F., Lu D. Q. An optimization of eigenfunction expansion method for the interaction of water waves with an elastic plate [J]. Journal of Hydrodynamics, 2009, 21(4): 526–530.CrossRefGoogle Scholar
  10. [10]
    Karmakar D., Sahoo T. Gravity wave interaction with floating membrane due to abrupt change in water depth [J]. Ocean Engineering, 2008, 35(7): 598–615.CrossRefGoogle Scholar
  11. [11]
    Dhillon H., Banerjea S., Mandal B. N. Water wave scattering by a finite dock over a step-type bottom topography [J]. Ocean Engineering, 2016, 113: 1–10.CrossRefGoogle Scholar
  12. [12]
    Guo Y., Liu Y., Meng X. Oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography [J]. Acta Oceanologica Sinica, 2016, 35: 113–121.Google Scholar
  13. [13]
    Das S., Bora S. N. Reflection of oblique ocean water waves by a vertical porous structure placed on a multi-step impermeable bottom [J]. Applied Ocean Research, 2014, 47: 373–385.CrossRefGoogle Scholar
  14. [14]
    Meng Q. R., Lu D. Q. Scattering of gravity waves by a porous rectangular barrier on a seabed [J]. Journal of Hydrodynamics, 2016, 28(3): 519–522.CrossRefGoogle Scholar
  15. [15]
    Zhao W., Taylor P. H., Wolgamot H. A. et al. Amplification of random wave run-up on the front face of a box driven by tertiary wave interaction [J]. Journal of Fluid Mechanics, 2019, 869: 706–725.CrossRefGoogle Scholar
  16. [16]
    Liu Y., Li Y., Teng B. Wave interaction with a new type perforated breakwater [J]. Acta Mechanica Sinica, 2007, 23(4): 351–358.CrossRefGoogle Scholar
  17. [17]
    Liu Y., Li Y., Teng B. Interaction between obliquely incident waves and an infinite array of multi-chamber perforated caissons [J]. Journal of Engineering Mathematics, 2012, 74: 1–18.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Bhattacharjee J., Soares C. G. Wave interaction with a floating rectangular box near a vertical wall with step type bottom topography [J]. Journal of Hydrodynamics, 2010, 22: 91–96.CrossRefGoogle Scholar
  19. [19]
    Behera H., Kaligatla R. B., Sahoo T. Wave trapping by porous barrier in the presence of step type bottom [J]. Wave Motion, 2015, 57: 219–230.MathSciNetCrossRefGoogle Scholar
  20. [20]
    Koley S., Sahoo T. Oblique wave trapping by vertical permeable membrane barriers located near a wall [J]. Journal of Marine Science and Application, 2017, 16(4): 490–501.CrossRefGoogle Scholar
  21. [21]
    Jung T. H., Suh K. D., Lee S. O. et al. Transformation of long waves propagating over trench [J]. Journal of Korean Society of Coastal and Ocean Engineers, 2007, 19: 228–236.Google Scholar
  22. [22]
    Roy R., Chakraborty R., Mandal B. N. Propagation of water waves over an asymmetrical rectangular trench [J]. The Quarterly Journal of Mechanics and Applied Mathematics, 2016, 70(1): 49–64.MathSciNetzbMATHGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoparPunjabIndia

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