Abstract
Havelock’s type of expansion theorems, for an integrable function having a single discontinuity point in the domain where it is defined, are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities. Also, complete analytical solutions are obtained for the boundary-value problems dealing with the generation or scattering of axi-symmetric water waves by a system of permeable and impermeable co-axial cylinders. Various results concerning the generation and reflection of the axisymmetric surface or interfacial waves are derived in terms of Bessel functions. The resonance conditions within the trapped region are obtained in various cases. Further, expansions for multipole-line-source oblique-wave potentials are derived for both the cases of finite and infinite depth depending on the existence of the source point in a two-layered fluid.
Similar content being viewed by others
References
T.H. Havelock (1929) ArticleTitleForced surface wave on water Phil. Mag. 8 569–576
C.M. Linton M. McIver (1995) ArticleTitleThe interaction of waves with horizontal cylinders in two-layer fluids J. Fluid Mech. 304 213–229
O.V. Motygin N.G. Kuznetsov (1997) ArticleTitleThe wave resistance of a two-dimensional body moving forward in a two-layer fluid J. Engng. Math. 35 53–72 Occurrence Handle10.1023/A:1004218330756
P.K. Kundu I.M. Cohen (2002) Fluid Mechanics Academic Press New York 730
R.W. Yeung and T. Nguyen, Radiation and diffraction of waves in a two-layer fluid. Proc. 22nd Symposium on Naval Hydrodynamics Washington, DC: National Academy Press (1999) pp. 875–891.
J.R. Cadby C. M. Linton (2000) ArticleTitleThree dimensional water wave scattering in two-layer fluids J. Fluid Mech. 423 155–173 Occurrence Handle10.1017/S0022112000002007
G. Zilman T. Miloh (1995) ArticleTitleHydrodynamics of a body moving over a mud layer-Part I:, Wave resistance J. Ship Res. 39 194–201
G. Zilman L. Kagan T. Miloh (1996) ArticleTitleHydrodynamics of a body moving over a mud layer-Part II: Added-mass and damping coefficients J. Ship Res. 40 39–45
E. Barthelemy A. Kabbaj J.P. Germain (2000) ArticleTitleLong surface wave scattered by a step in a two-layer fluid Fluid Dynam. Res. 26 235–255 Occurrence Handle10.1016/S0169-5983(99)00025-8
C.M. Linton J.R. Cadby (2002) ArticleTitleScattering of oblique waves in a two-layer fluid J. Fluid Mech. 461 343–364 Occurrence Handle10.1017/S002211200200842X
B.N. Mandal A. Chakrabarti (2003) ArticleTitleA generalization to the hybrid Fourier transform and its application Appl. Math. Lett. 16 703–708 Occurrence Handle10.1016/S0893-9659(03)00070-3
A.T. Chwang (1983) ArticleTitleA porous wavemaker theory J. Fluid Mech. 132 395–406
A.T. Chwang W. Li (1983) ArticleTitleA piston-type porous wavemaker theory J. Engng. Math. 17 301–313
M.M. Lee A.T. Chwang (2000) ArticleTitleScattering and radiation of water waves by permeable barriers Phys. Fluids 12 54–65 Occurrence Handle10.1063/1.870284
H.H. Sherief M.S. Faltas E.I. Saad (2003) ArticleTitleForced gravity waves in two-layered fluids with the upper fluid having a free surface Can. J. Phys. 81 675–689 Occurrence Handle10.1139/p02-133
T. Sahoo (1998) ArticleTitleOn the generation of water waves by cylindrical porous wavemaker Acta Mech. 126 231–239 Occurrence Handle10.1007/BF01172810
J.V. Wehausen and E.V. Laitone, Surface waves. In: S. Flugge (ed.), Handbuck der Physik, vol. 9, Springer Verlag (1960) pp. 446–778.
X. Yu A.T. Chwang (1994) ArticleTitleWave induced oscillation in harbour with porous breakwaters J. Waterway, Port, Coast. and Ocean Engrg. 120 125–144
C.K. Sollitt R.H. Cross (1972) Wave transmission through permeable breakwaters Canada Vancouver 1827–46
A.T. Chwang A.T. Chan (1998) ArticleTitleInteraction between porous media and wave motion Ann. Rev. Fluid Mech. 30 53–84 Occurrence Handle10.1146/annurev.fluid.30.1.53
T. Sahoo M.M. Lee A.T. Chwang (2000) ArticleTitleTrapping and generation of waves by vertical porous structure J. Engng. Mech. 126 1074–1082 Occurrence Handle10.1061/(ASCE)0733-9399(2000)126:10(1074)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Manam, S.R., Sahoo, T. Waves Past Porous Structures in a Two-layer Fluid. J Eng Math 52, 355–377 (2005). https://doi.org/10.1007/s10665-005-0190-9
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10665-005-0190-9