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Linear Gravity Waves over Rigid, Porous Bottoms

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Dynamics of Surface Waves in Coastal Waters

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Abstract

Taking aim at real sea beds and using Green’s formula, two different models involving the mild-slope equations and the general continuity of the variation of wave numbers are presented to study linear gravity wave transformation over rigid, porous bottoms. The first specializes in that both the water and the porous layers consist of two kind of components: the slowly varying one whose horizontal length scale is longer than the surface wave length, and the fast varying one with the horizontal length scale as the surface wave length. The amplitude of the fast varying component is, however, smaller than the surface wave length. In addition, the fast varying component of the lower boundary surface of the porous layer is one order of magnitude smaller than that of the water depth. Including the effect of evanescent modes, the second depends on a generally varying bottom without prescribed assumption, and covers a number of special and typical mild-slope equations with and without porous layers.

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References

  1. Chen Q (2006). Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. J Engng Mech 132: 220–230

    Article  Google Scholar 

  2. Chwang A T, Chan A T (1998). Interaction between porous media and wave motion. Annu Rev Fluid Mechanics 30: 53–84

    Article  MathSciNet  ADS  Google Scholar 

  3. Dean R G, Dalrymple R A (1984). Water wave mechanics for engineers and scientists. Prentice-Hall, New Jersey

    Google Scholar 

  4. Dingemans M W (1997). Water wave propagation over uneven bottom. World Scientific, Singapore

    Book  Google Scholar 

  5. Flaten G, Rygg O B (1991). Dispersive shallow water waves over a porous sea bed. Coastal Engng 15: 347–369

    Article  Google Scholar 

  6. Gu Z, Wang H (1991). Gravity waves over porous bottoms. Coastal Engng 15: 497–524

    Article  Google Scholar 

  7. Hsiao S, Liu P L-F, Chen Y (2002). Nonlinear water waves propagating over a permeable bed. Proc R Soc Lond A 458: 1291–1322

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Hsu T-J, Sakakiyama T, Liu PL-F (2002). A numerical model for wave motions and turbulence flows in front of a composite breakwater. Coastal Engng 46: 25–50

    Article  Google Scholar 

  9. Huang H (2004). Composite equations of water waves over uneven and porous seabed (in Chinese). Acta Mech Sin 36: 455–459

    Google Scholar 

  10. Kirby J T (1986). On the gradual reflection of weakly nonlinear stokes waves in regions with varying topography. J Fluid Mech 162: 187–209

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Lara J L, Garcia N, Losada I J (2006). RANS modelling applied to random wave interaction with submerged permeable structures. Coastal Engng 53: 395–417

    Article  Google Scholar 

  12. Losada I J (2001). Recent advances in the modeling of wave and permeable structure interaction. In: Liu PL-F (ed) Advances in coastal and occan engineering, Vol 7. World Scientific, Singapore

    Google Scholar 

  13. Mase H, Takeba K, Oki S I (1995). Wave equation over permeable rippled bed and analysis of Bragg scattering of surface gravity waves. J Hydra Res 33: 789–812

    Article  Google Scholar 

  14. Rojanakamthorn S, Isobe M, Watanabe A (1989). A mathematical model of wave transformation over a submerged breakwater. Coastal Engng Jap 31: 209–234

    Google Scholar 

  15. Silva R, Salles P, Palacio A (2002). Linear waves propagating over a rapidly varying finite bed. Coastal Engng 44: 239–260

    Article  Google Scholar 

  16. Silva R, Salles P, Govaere G (2003). Extended solution for waves traveling over a rapidly changing porous bottom. Coastal Engng 30: 437–452

    Google Scholar 

  17. Sollitt C K, Cross R H (1972). Wave transmission through permeable breakwaters. In: Proceedings of the 13th international conference on coastal engineering. ASCE, New York: 1837–1846

    Google Scholar 

  18. Suo Y H, Huang H (2004). A general linear wave theory for water waves propagating over uneven porous bottoms. Chin Ocean Engng 18: 163–171

    Google Scholar 

  19. Ting C L, Lin M C, Kuo C L (2000). Bragg scattering of surface waves over permeable rippled beds with current. Phys Fluids 12: 1382–1388

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Tsai C P, Chen H B, Lee F C (2006). Wave transformation over submerged permeable break-water on porous bottom. Ocean Engng 33: 1623–1643

    Article  Google Scholar 

  21. Van Gent M R A (1994). The modelling of wave action on and in coastal structures. Coastal Engng 22: 311–339

    Article  Google Scholar 

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P.R. China

    Prof. Hu Huang

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  1. Prof. Hu Huang
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© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Huang, H. (2009). Linear Gravity Waves over Rigid, Porous Bottoms. In: Dynamics of Surface Waves in Coastal Waters. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88831-4_5

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  • DOI: https://doi.org/10.1007/978-3-540-88831-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88830-7

  • Online ISBN: 978-3-540-88831-4

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