DOI QR코드

DOI QR Code

Investigation of surface-piercing fixed structures with different shapes for Bragg reflection of water waves

  • Ding, Wei-Wei (School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University) ;
  • Zou, Zao-Jian (School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University) ;
  • Wu, Jing-Ping (School of Transportation, Wuhan University of Technology) ;
  • Huang, Bai-Gang (School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University)
  • Received : 2018.09.22
  • Accepted : 2019.03.27
  • Published : 2019.02.18

Abstract

Bragg reflection of water waves by three kinds of surface-piercing fixed structures with rectangular, cosinoidal and triangular shapes is studied. Boundary element method is used to analyze the wave scattering by these structures based on the linear wave theory. Results of reflection and transmission coefficients are validated by comparing with those available in literature. These structures with proper configurations are proved to be effective in attenuating waves by using Bragg reflection, and the triangular structures are found to be the best choices among the structures with same width and same area. Systematic calculations are then carried out for the triangular structures by varying the number, the draft, the width, the gap and the combination of width and gap of the structures to analyze their influences on the characteristics of Bragg reflection. The results are of reference values for design of the structures to attenuate waves based on the Bragg reflection.

Keywords

References

  1. Bailard, J.A., DeVries, J.W., Kirby, J.T., Guza, R.T., 1990. Bragg reflection breakwater: a new shore protection method?. In: Proc. 22nd Int. Conf. on Coastal Eng., ASCE, N.Y., U.S, pp. 1702-1715.
  2. Bailard, J.A., DeVries, J.W., Kirby, J.T., 1992. Considerations in using Bragg reflection for storm erosion protection. J. Waterw. Port, Coast. Ocean Eng. 118 (1), 62-74. https://doi.org/10.1061/(ASCE)0733-950X(1992)118:1(62)
  3. Chang, H.K., Liou, J.C., 2007. Long wave reflection from submerged trapezoidal breakwaters. Ocean Eng. 34 (1), 185-191. https://doi.org/10.1016/j.oceaneng.2005.11.017
  4. Cho, Y.S., Lee, C., 2000. Resonant reflection of waves over sinusoidally varying topographies. J. Coast. Res. 16 (3), 870-876.
  5. Cho, Y.S., Jeong,W.C.,Woo, S.B., 2004. Finite element method for strong reflection of water waves. Ocean Eng. 31, 653-667. https://doi.org/10.1016/j.oceaneng.2003.07.007
  6. Dalrymple, R.A., Kirby, J.T., 1986. Water waves over ripples. J. Waterw. Port, Coast. Ocean Eng. 112 (2), 309-319. https://doi.org/10.1061/(ASCE)0733-950X(1986)112:2(309)
  7. Ding, W.W., Zou, Z.J., Wu, J.P., 2018. Bragg reflection of water waves by multiple composite flexible membranes. Int. J. Offshore Polar Eng. 28 (02), 135-142. https://doi.org/10.17736/ijope.2018.ak24
  8. Garnaud, X., Mei, C.C., 2010. Bragg scattering and wave-power extraction by an array of small buoys. Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 466 (2113), 79-106.
  9. Hsu, T.W., Chang, H.K., Tsai, L.H., 2002. Bragg reflection of waves by different shapes of artificial bars. China Ocean Eng. 16 (3), 343-358. https://doi.org/10.3321/j.issn:0890-5487.2002.03.007
  10. Hsu, T.W., Tsai, L.H., Huang, Y.T., 2003. Bragg scattering of water waves by multiply composite artificial bars. Coast Eng. J. 45 (2), 235-253. https://doi.org/10.1142/S0578563403000750
  11. Jeon, C.H., Cho, Y.S., 2006. Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters. Ocean Eng. 33, 2067-2082. https://doi.org/10.1016/j.oceaneng.2005.07.013
  12. Karmakar, D., Bhattacharjee, J., Guedes Soares, C., 2013. Scattering of gravity waves by multiple surface-piercing floating membrane. Appl. Ocean Res. 39, 40-52. https://doi.org/10.1016/j.apor.2012.10.001
  13. Kar, P., Koley, S., Sahoo, T., 2018. Scattering of surface gravity waves over a pair of trenches. Appl. Math. Model. 62, 303-320. https://doi.org/10.1016/j.apm.2018.06.002
  14. Linton, C.M., 2011. Water waves over arrays of horizontal cylinders: band gaps and Bragg resonance. J. Fluid Mech. 670, 504-526. https://doi.org/10.1017/S0022112010005471
  15. Liu, P.L.-F., Abbaspour, M., 1982. An integral equation method for the diffraction of oblique waves by an infinite cylinder. Int. J. Numer. Methods Eng. 18, 1497-1504. https://doi.org/10.1002/nme.1620181005
  16. Liu, H.W., Luo, H., Zeng, H.D., 2014. Optimal collocation of three kinds of Bragg breakwaters for Bragg resonant reflection by long waves. J. Waterw. Port, Coast. Ocean Eng. 141 (3), 04014039. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000278
  17. Liu, H.W., Shi, Y.P., Cao, D.Q., 2015. Optimization of parabolic bars for maximum Bragg resonant reflection of long waves. J. Hydrodyn. 27 (3), 373-382. https://doi.org/10.1016/S1001-6058(15)60495-4
  18. Liu, Y., Li, H.J., Zhu, L., 2016. Bragg reflection of water waves by multiple submerged semi-circular breakwaters. Appl. Ocean Res. 56, 67-78. https://doi.org/10.1016/j.apor.2016.01.008
  19. Mei, C.C., Hara, T., Naciri, M., 1988. Note on Bragg scattering of water waves by parallel bars on the seabed. J. Fluid Mech. 186, 147-162. https://doi.org/10.1017/S0022112088000084
  20. Ouyang, H.T., Chen, K.H., Tsai, C.M., 2015. Investigation on Bragg reflection of surface water waves induced by a train of fixed floating pontoon breakwaters. Int. J. Nav. Archit. Ocean Eng. 7, 951-963. https://doi.org/10.1515/ijnaoe-2015-0066
  21. Shih, R.S., Weng, W.K., 2016. Experimental determination of the performance characteristics of an undulating submerged obstacle. Ships Offshore Struct. 11 (2), 129-141. https://doi.org/10.1080/17445302.2014.967993
  22. Teng, B., Gou, Y., 2017. BEM for wave interaction with structures and low storage accelerated methods for large scale computation. J. Hydrodyn., Ser. B 29 (5), 748-762. https://doi.org/10.1016/S1001-6058(16)60786-2
  23. Tsai, L.H., Kuo, Y.S., Lan, Y.J., Hsu, T.W., Chen, W.J., 2011. Investigation of multiply composite artificial bars for Bragg scattering of water waves. Coast Eng. J. 53 (4), 521-548. https://doi.org/10.1142/S0578563411002446
  24. Tsai, L.H., Wen, C.C., 2010. Design of a series of submerged breakwaters for coastal protection against waves. China Ocean Eng. 24 (3), 553-564.
  25. Wen, C.C., Tsai, L.H., 2008. Numerical simulation of Bragg reflection based on linear waves propagation over a series of rectangular seabed. China Ocean Eng. 22 (1), 71-86.
  26. Zeng, H.D., Qin, B., Zhang, J.H., 2017. Optimal collocation of Bragg breakwaters with rectangular bars on sloping seabed for Bragg resonant reflection by long waves. Ocean Eng. 130, 156-165. https://doi.org/10.1016/j.oceaneng.2016.11.066

Cited by

  1. Bragg Reflections of Oblique Water Waves by Periodic Surface-Piercing and Submerged Breakwaters vol.8, pp.7, 2019, https://doi.org/10.3390/jmse8070522
  2. Bragg scattering of long waves by an array of floating flexible plates in the presence of multiple submerged trenches vol.32, pp.9, 2019, https://doi.org/10.1063/5.0017930
  3. Gravity Wave Trapping by Series of Horizontally Stratified Wave Absorbers Away From Seawall vol.142, pp.6, 2019, https://doi.org/10.1115/1.4047104
  4. Multiple stopbands and wavefield asymmetry of surface water waves in non-Bragg structures vol.11, pp.1, 2019, https://doi.org/10.1063/5.0032151