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The interaction of waves with horizontal cylinders in two-layer fluids

  • C. M. Linton (a1) and M. McIver (a1)


We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise. These relations are systematically extended to the two-fluid case. It is shown that for symmetric bodies the solutions to scattering problems where the incident wave has wavenumber K and those where it has wavenumber k are related so that the solution to both can be found by just solving one of them. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are then solved using multipole expansions.



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Baines, P. G. 1984 A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127168.
Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559592.
Dean, W. R. 1948 On the reflexion of surface waves by a submerged circular cylinder. Proc. Comb. Phil. Soc. 44, 483491.
Evans, D. V. & Linton, C. M. 1989 Active devices for the reduction in wave intensity. Appl. Ocean Res. 11, 2632.
Friis, A., Grue, J. & Palm, E. 1991 Application of Fourier transform to the second order 2D wave diffraction problem. In M. P. Tulin's Festschrift: Mathematical Approaches In Hydrodynamics (ed. T. Miloh), pp. 209227.
Siam. Gradshteyn, I. S. & Ryzhik, I. M. 1965 Tables of Integrals, Series and Products. Academic Press.
Kassem, S. E. 1982 Multipole expansions for two superposed fluids, each of finite depth. Math. Proc. Camb. Phil. Soc. 91, 323329.
Keulegan, G. H. 1953 Characteristics of internal solitary waves. J. Res. Natl Bur. Stand. 51, 133.
Lamb, H. 1932 Hydrodynamics (6th edn). Cambridge University Press. Reprinted 1993.
Long, R. R. 1956 Solitary waves in one- and two-fluid systems. Tellus 8, 460.
Newman, J. N. 1976 The interaction of stationary vessels with regular waves. In Proc. llth Symp. on Naval Hydrodynamics, London.
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441455. Reprinted in Mathematical and Physical Papers, Vol. 1, pp. 314–326. Cambridge University Press.
Sturova, I. V. 1994 Hydrodynamic forces on a submerged cylinder advancing in waves of two-layer fluids. In Proc. 9th Intl Workshop on Water Waves and Floating Bodies, Kuju, Japan, pp. 199203.
Thorne, R. C. 1953 Multipole expansions in the theory of surface waves. Proc. Camb. Phil. Soc. 49, 707716.
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged circular cylinder I. Proc. Camb. Phil. Soc. 46, 141152.
Wu, J.-H. 1992 The second order wave loads on bodies in stratified ocean. In Proc. 7th Intl Workshop on Water Waves and Floating Bodies, Val de Reuil, France, pp. 297301.
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The interaction of waves with horizontal cylinders in two-layer fluids

  • C. M. Linton (a1) and M. McIver (a1)


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