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Citation:
　P. MAITI,B. N. Mandal and U. Basu.Wave scattering by undulating bed topography in a two-layer ocean[J].Journal of Marine Science and Application,2009,(3):183-195.
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Wave scattering by undulating bed topography in a two-layer ocean

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Title:
Wave scattering by undulating bed topography in a two-layer ocean
Author(s):
P. MAITI;  B. N. Mandal and U. Basu
Affilations:
Author(s):
P. MAITI;  B. N. Mandal and U. Basu
1. Department of Mathematics, Jadavpur University, Kolkata 700032, India
2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
3. Department of Applied Mathematics, Calcutta University, Kolkata 700009, India
Keywords:
two-layer ocean;  wave scattering;  bottom undulations;  reflection and transmission coefficients
分类号:
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DOI:
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Abstract:
The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape function. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.

References:

[1] MILES J W. Oblique surface-wave diffraction by a cylindrical obstacle[J]. Dynamics of Atmospheres and Oceans, 1981, 6(2): 121-123.
[2] DAVIES A G. The reflection of wave energy by undulations on the seabed[J]. Dynamics of Atmospheres and Oceans, 1982, 6(4): 207-232.
[3] MANDAL B N, BASU U. A note on oblique water wave diffraction by a cylindrical deformation of the bottom in the presence of surface tension[J]. Arch. Mech., 1990, 42: 723-727.
[4] LAMB H. Hydrodynamics[M]. Cambridge: Cambridge University Press, 1995.
[5] LINTON C M, MCIVER M. The interaction of waves with horizontal cylinders in two-layer fluids[J]. Journal of Fluid Mechanics, 1995, 304: 213-229.
[6] CADBY J R, LINTON C M. Three-dimensional water-wave scattering in two-layer fluids[J]. Journal of Fluid Mechanics, 2000, 423: 155-173.
[7] SHERIEF H H, FALTAS M S, SAAD E I. Forced gravity waves in two-layered fluids with the upper fluid having a free surface[J]. Canadian Journal of Physics, 2003, 81(4): 675-689.
[8] SHERIEF H H, FALTAS M S, SAAD E I. Axisymmetric gravity waves in two-layered fluids with the upper fluid having a free surface[J]. Wave Motion, 2004, 40: 143-161.
[9] SHAW D C. Perturbational results for diffraction of water waves by nearly vertical barriers[J]. IMA Journal of Applied Mathematics, 1985, 34(1): 99-117.
[10] MANDAL B N, CHAKRABARTI A. A note on diffraction of water waves by a nearly vertical barrier[J]. IMA Journal of Applied Mathematics, 1989, 43(2): 157-165.
[11] MANDAL B N, KUNDU P K. Scattering of water waves by a submerged nearly vertical plate[J]. SIAM Journal on Applied Mathematics, 1990, 50(5): 1221-1231.
[12] RHODES-ROBINSON P F. On wave motion in a two-layered liquid of infinite depth in the presence of surface and interfacial tension[J]. The Journal of the Australian Mathematical Society, 1994, 35: 302-322.
[13] TEN I, KASHIWAGI M. Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part I. Radiation problem[J]. Journal of Marine Science and Technology, 2004, 9: 127-141.

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Last Update: 2010-05-02