Waves Past Porous Structures in a Two-layer Fluid
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.
Keywordsporous barriers reflection coefficient source potentials surface and interfacial waves wave trapping
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- 1.Havelock, T.H. 1929Forced surface wave on waterPhil. Mag.8569576Google Scholar
- 2.Linton, C.M., McIver, M. 1995The interaction of waves with horizontal cylinders in two-layer fluidsJ. Fluid Mech.304213229Google Scholar
- 4.Kundu, P.K., Cohen, I.M. 2002Fluid MechanicsAcademic PressNew York730Google Scholar
- 5.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.Google Scholar
- 7.Zilman, G., Miloh, T. 1995Hydrodynamics of a body moving over a mud layer-Part I:, Wave resistanceJ. Ship Res.39194201Google Scholar
- 8.Zilman, G., Kagan, L., Miloh, T. 1996Hydrodynamics of a body moving over a mud layer-Part II: Added-mass and damping coefficientsJ. Ship Res.403945Google Scholar
- 12.Chwang, A.T. 1983A porous wavemaker theoryJ. Fluid Mech.132395406Google Scholar
- 13.Chwang, A.T., Li, W. 1983A piston-type porous wavemaker theoryJ. Engng. Math.17301313Google Scholar
- 17.J.V. Wehausen and E.V. Laitone, Surface waves. In: S. Flugge (ed.), Handbuck der Physik, vol. 9, Springer Verlag (1960) pp. 446–778.Google Scholar
- 18.Yu, X., Chwang, A.T. 1994Wave induced oscillation in harbour with porous breakwatersJ. Waterway, Port, Coast. and Ocean Engrg.120125144Google Scholar
- 19.Sollitt, C.K., Cross, R.H. 1972Wave transmission through permeable breakwatersCanadaVancouver182746Proc. 13th ASCE Conf. Coastal Eng.Google Scholar