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Reflection and transmission from porous structures under oblique wave attack

Published online by Cambridge University Press:  26 April 2006

Robert A. Dalrymple ,
Miguel A. Losada  and
P. A. Martin
Robert A. Dalrymple
Affiliation:
Center for Applied Coastal Research, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA
Miguel A. Losada
Affiliation:
Departamento de Ciencias y Tecnicas del Agua y del Medio Ambiente, University of Cantabria, Santander, Spain
P. A. Martin
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.

Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.

An important parameter in this problem is Γ2 = ω2h(s - if)/g, where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ2.

For an infinite number of values of ΓF2, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ2, it is shown that the wave modes can swap their identity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 625 - 644
Copyright
© 1991 Cambridge University Press

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References

Churchill, R. V.: 1960 Complex Variables and Applications. McGraw-Hill.
Cbaik, A. D. D.: 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Dattatri, J., Raman, H. & Shankar, J. N., 1978 Performance characteristics of submerged breakwaters. In Proc. 16th Coastal Engng Conf., Hamburg, pp. 2153–2171. ASCE.
Hannoura, A. A. & McCorquodale, I. A., 1978 Virtual mass of coarse granular media. J. Waterways, Ports, Coastal Ocean Engng Div., ASCE 104, 191–200.Google Scholar
Iwasaki, T. & Numata, A., 1970 Experimental studies on wave transmission of a permeable breakwater constructed by artificial blocks. Coastal Engng Japan 13, 25–29.Google Scholar
John, F.: 1950 On the motion of floating bodies, II. Commun. Pure Appl. Maths 3, 45–101.Google Scholar
Le Méhauté, B. 1957 Perméabilité des digues en enrochements aux ondes de gravité périodiques. Houille Blanche 6, 903–919.Google Scholar
Madsen, O. S.: 1974 Wave transmission through porous structures. J. Waterways, Ports, Coastal Ocean Engng Div., A8CE 100, 169–188.Google Scholar
Madsen, O. S. & White, S. M., 1976 Wave transmission through trapezoidal breakwaters. In Proc. 15th Coastal Engng Conf., Honolulu, pp. 2662–2676. ASCE.
Madsen, P. A.: 1983 Wave reflection from a vertical permeable wave absorber. Coastal Engng 7, 381–396.Google Scholar
Mathieu, J. P.: 1975 Optics. Pergamon.
Miles, J. W.: 1981 Oblique surface-wave diffraction by a cylindrical obstacle. Dyn. Atmos. Oceans 6, 121–123.Google Scholar
Moese, P. M. & Ingard, K. U., 1968 Theoretical Acoustics. Princeton University Press.
Sollitt, C. K. & Cross, R. H., 1972 Wave transmission through permeable breakwaters. In Proc. 13th Coastal Engng Conf., Vancouver, pp. 1827–1846.Google Scholar
Asce, Sollitt, C. K. & Cross, R. H. 1976 Wave reflection and transmission at permeable breakwaters. Tech. Paper 76–8. US Army Corps of Engineers, Coastal Engineering Research Center.
Sulisz, W.: 1985 Wave reflection and transmission at permeable breakwaters of arbitrary cross section. Coastal Engng 9, 371–386.Google Scholar
Tester, B. J.: 1973 The optimization of modal sound attenuation in ducts, in the absence of mean flow. J. Sound Vib. 27, 477–513.Google Scholar
Yeh, P.: 1988 Optical Waves in Layered Media. John Wiley & Sons.