Citation:
Smrutiranjan Mohapatra.Scattering of Surface Waves by the Edge of a Small Undulation on a Porous Bed in an Ocean with Ice-cover[J].Journal of Marine Science and Application,2014,(2):167-172.[doi:10.1007/s11804-014-1241-2]
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Scattering of Surface Waves by the Edge of a Small Undulation on a Porous Bed in an Ocean with Ice-cover
Smrutiranjan Mohapatra.Scattering of Surface Waves by the Edge of a Small Undulation on a Porous Bed in an Ocean with Ice-cover[J].Journal of Marine Science and Application,2014,(2):167-172.[doi:10.1007/s11804-014-1241-2]
Info
- Title:
- Scattering of Surface Waves by the Edge of a Small Undulation on a Porous Bed in an Ocean with Ice-cover
- Author(s):
- Smrutiranjan Mohapatra
- Affilations:
- Keywords:
- porous bed; ice-cover; surface waves; bottom undulation; Green’s function; perturbation technique; reflection and transmission coefficients
- DOI:
- 10.1007/s11804-014-1241-2
- Abstract:
- Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace’s equation by a method based on Green’s integral theorem with the introduction of appropriate Green’s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.
References:
Chakrabarti A (2000). On the solution of the problem of scattering of surface-water waves by the edge of an ice-cover. Proceedings of the Royal Society of London Series A, 456(1997), 1087-1099.
Davies AG (1982). The reflection of wave energy by undulations of the sea bed. Dynamics of Atmosphere and Oceans, 6(4), 207-232.
Fox C, Squire VA (1994). On the oblique reflection and transmission of ocean waves at shore fast sea ice. Phil. Trans. R. Soc. Lond, 347(A), 185-218.
Linton CM, Chung H (2003). Reflection and transmission at the ocean/sea-ice boundary. Wave Motion, 38(1), 43-52.
Mandal BN, Basu U (2004). Wave diffraction by a small elevation of the bottom of an ocean with an ice-cover. Archive of Applied Mechanics, 76(11-12), 812-822.
Martha SC, Bora SN, Chakrabarti A (2007). Oblique water-wave scattering by small undulation on a porous sea-bed. Applied Ocean Research, 29(1-2), 86-90.
Mei CC (1985). Resonant reflection of surface water waves by periodic sandbars. Journal of Fluid Mechanics, 152, 315-335.
Miles JW (1981). Oblique surface wave diffraction by a cylindrical obstacle. Journal of Atmosphere and Oceans, 6(2), 121-123.
Porter BR, Porter D (2003). Scattered and free waves over periodic beds. Journal of Fluid Mechanics, 483, 129-163.
Rhodes-Robinson PF (1970). Fundamental singularities in the theory of water waves with surface tension. Bull. Ausral. Math. Soc., 2, 317-333.
Silva R, Salles P, Palacio A (2002). Linear wave propagating over a rapidly varying finite porous bed. Coastal Engineering, 44(3), 239-260.
Zhu Shutang (2001). Water waves within a porous medium on an undulating bed. Coastal Engineering, 42(1), 87-101.
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