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Wave Interaction with an Emerged Porous Media

  • I. Magdalena (a1), S. R. Pudjaprasetya (a1) and L. H. Wiryanto (a1)
Abstract
Abstract

In this paper, we study wave interaction with an emerged porous media. The governing equation is shallow water equations with a friction term of the linearized Dupuit-Forcheimer’s formula. From the continuity of surface and horizontal flux, we derived the wave reflection and transmission coefficient formulas. They are similar with the corresponding formulas of the submerged solid bar breakwater. We solve the equations numerically using finite volume method on a staggered grid. The numerical wave reduction in the porous media confirms the analytical wave transmission curve.

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Corresponding author
Corresponding author. Email: ikha.magdalena@yahoo.com
Email: sr_pudjap@math.itb.ac.is
References
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[1]Calabrese M., Vicinanza D. and Buccino M., 2D Wave setup behind submerged breakwa-ters, Ocean Eng., 35 (2008), pp. 10151028.
[2]Chwang A. T. and Chan A. T., Interaction between porous media and wave motion, Annu. Rev. Fluid Mech, 30 (1998), pp. 5384.
[3]Dalrymple R. A., Losada M. A. and Martin P. A., Reflection and transmission from porous structures under oblique wave attack, J. Fluid Mech., 224 (1991), pp. 625644.
[4]Dean R. G. and Dalrymple R. A., Water Wave Mechanics for Engineers and Scientists, World Scientific, 1991.
[5]van Groesen Andonowati E., Similarities between optical and surface water waves, J. In-donesia Math Soc., 8(3) (2002), pp. 18.
[6]Gu Z. AND Wang H., Gravity waves over porous bottoms, Coastal Eng., 15 (1991), pp. 497524.
[7]Gu Z. and Wang H., Numerical modeling for wave energy dissipation within porous submerged breakwaters of irregular cross section, Coastal Eng., 90 (1992), pp. 11891198.
[8]Kobayashi Wurjanto N., Wave transmission over submerged breakwaters, J. Waterways Port Coastal Eng. ASCE, 115(5) (1989), pp. 662680.
[9]Liu P. L. F. and Wen Jiangang, Nonlinear diffusive surface waves in porous media, J. Fluid Mech., 347 (1997), pp. 119139.
[10]Liu P. L. F., Lin P., Chang and Tsutomu Sakakiyama K. A., Numerical modeling of wave interaction with porous structures, J. Waterway Port Coastal Ocean Eng., (1999), pp. 322330.
[11]Lynett P. J., Liu P. L. F., Losada I. J. and Vidal C., Solitary wave interaction with porous breakwaters, J. Waterway Port Coastal Ocean Eng., (2000), pp. 314322.
[12]Madsen O. S., Wave transmission through porous structures, J. Waterways Harbors Coastal Eng. Division, ASCE, 100 (1974), pp. 169188.
[13]Mei C. C., The Applied Dynamics of Ocean Surface Waves, World Scientific, 1989.
[14]Pudjaprasetya S. R. and Chendra H. D., An optimal dimension of submerged parallel bars as a wave reflector, Bull. Malaysian Mathematical Sci. Soc., 32(1) (2009), pp. 5562.
[15]Pudjaprasetya S. R. and Magdalena I., Momentum conservative scheme for dam break and wave run up simulations, East Asian J. Appl. Math.,4 (2014), pp. 152165.
[16]Pudjaprasetya S. R. and Magdalena I., Wave energy dissipation over porous media, Appl. Math. Sci., 7(59) (2013), pp. 29252937.
[17]Sollitt C. K. and Cross R. H., Long-wave transmission through porous breakwaters, Proc. 13th Coastal Eng. Conf., ASCE, 3 (1972), pp. 18271846.
[18]Stelling G. S. and Duinmeijer S. P. A., A staggered conservative scheme for every Froude number in rapidly varied shallow water flows, Int. J. Numer. Meth. Fluids, 43 (2003), pp. 13291354.
[19]Sulisz W., Wave reflection and transmission at permeable breakwaters of arbitrary cross-section, Coastal Eng., 9 (1985), pp. 371386.
[20]Van Gent M. R. A., Wave Interaction with Permeable Coastal Structure, PhD thesis, Delft University, Delft, The Netherlands, 1995.
[21]Wiryanto L. H., Wave propagation passing over a submerged porous breakwater, J. Eng. Math., 70(2011), pp. 129136.
[22]Wiryanto L. H., Wave propagation over submerged bar, ITB J. Sci., 42A(2) (2010), pp. 8190.
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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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