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Wave Interaction with an Emerged Porous Media

Published online by Cambridge University Press:  03 June 2015

I. Magdalena ,
S. R. Pudjaprasetya  and
L. H. Wiryanto
I. Magdalena*
Affiliation:
Industrial & Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Jalan Ganesha 10, Bandung, West Java, Indonesia
S. R. Pudjaprasetya*
Affiliation:
Industrial & Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Jalan Ganesha 10, Bandung, West Java, Indonesia
L. H. Wiryanto
Affiliation:
Industrial & Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Jalan Ganesha 10, Bandung, West Java, Indonesia
*
Corresponding author. Email: ikha.magdalena@yahoo.com
Email: sr_pudjap@math.itb.ac.is
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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.

Keywords

76S0581U3035L02Emerged porous mediashallow water equationwave transmission coefficientwave reflection coefficient
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 680 - 692
Copyright
Copyright © Global-Science Press 2014

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References

[1]Calabrese, M., Vicinanza, D. and Buccino, M., 2D Wave setup behind submerged breakwa-ters, Ocean Eng., 35 (2008), pp. 1015–1028.Google Scholar
[2]Chwang, A. T. and Chan, A. T., Interaction between porous media and wave motion, Annu. Rev. Fluid Mech, 30 (1998), pp. 53–84.Google Scholar
[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. 625–644.CrossRefGoogle Scholar
[4]Dean, R. G. and Dalrymple, R. A., Water Wave Mechanics for Engineers and Scientists, World Scientific, 1991.Google Scholar
[5]van Groesen Andonowati, E., Similarities between optical and surface water waves, J. In-donesia Math Soc., 8(3) (2002), pp. 1–8.Google Scholar
[6]Gu, Z. and Wang, H., Gravity waves over porous bottoms, Coastal Eng., 15 (1991), pp. 497–524.Google Scholar
[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. 1189–1198.Google Scholar
[8]Kobayashi Wurjanto, N., Wave transmission over submerged breakwaters, J. Waterways Port Coastal Eng. ASCE, 115(5) (1989), pp. 662–680.Google Scholar
[9]Liu, P. L. F. and Wen, Jiangang, Nonlinear diffusive surface waves in porous media, J. Fluid Mech., 347 (1997), pp. 119–139.Google Scholar
[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. 322–330.Google Scholar
[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. 314–322.CrossRefGoogle Scholar
[12]Madsen, O. S., Wave transmission through porous structures, J. Waterways Harbors Coastal Eng. Division, ASCE, 100 (1974), pp. 169–188.Google Scholar
[13]Mei, C. C., The Applied Dynamics of Ocean Surface Waves, World Scientific, 1989.Google Scholar
[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. 55–62.Google Scholar
[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. 152–165.Google Scholar
[16]Pudjaprasetya, S. R. and Magdalena, I., Wave energy dissipation over porous media, Appl. Math. Sci., 7(59) (2013), pp. 2925–2937.Google Scholar
[17]Sollitt, C. K. and Cross, R. H., Long-wave transmission through porous breakwaters, Proc. 13th Coastal Eng. Conf., ASCE, 3 (1972), pp. 1827–1846.Google Scholar
[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. 1329–1354.Google Scholar
[19]Sulisz, W., Wave reflection and transmission at permeable breakwaters of arbitrary cross-section, Coastal Eng., 9 (1985), pp. 371–386.Google Scholar
[20]Van Gent, M. R. A., Wave Interaction with Permeable Coastal Structure, PhD thesis, Delft University, Delft, The Netherlands, 1995.Google Scholar
[21]Wiryanto, L. H., Wave propagation passing over a submerged porous breakwater, J. Eng. Math., 70(2011), pp. 129–136.Google Scholar
[22]Wiryanto, L. H., Wave propagation over submerged bar, ITB J. Sci., 42A(2) (2010), pp. 81–90.Google Scholar