Abstract
Water-wave scattering by porous bottom undulations of an ocean with an ice cover is investigated by perturbation analysis. The first-order reflection and transmission coefficients were obtained using Green’s integral theorem and Fourier transform technique. It is shown that the expressions for the first-order reflection and transmission coefficients are same for both the techniques. The first-order reflection coefficient is computed numerically and it is observed that the porosity of the ocean bottom has an effect on the reflection and transmission coefficients. The problem is also studied when the porosity parameter is a complex number. Numerical results are depicted graphically in a number of figures for different values of parameters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
A. Chakrabarti, On the solution of the problem of scattering of surface-water waves by the edge of an ice cover. Proc. R. Soc. Lond. A 456, 1087–1099 (2000)
C. Fox, V.A. Squire, On the oblique reflection and transmission of ocean waves at shore fast sea ice. Phil. Trans. R. Soc. Lond. A 347, 185–218 (1994)
C.M. Linton, H. Chung, Reflection and transmission at the ocean/sea-ice boundary. Wave Motion 38, 43–52 (2003)
D.V. Evans, T.V. Davies, Wave-ice interaction. Report no. 1313, Davidson Laboratory, Stevents Institutes of Technology, New Jersey, USA (1968)
H. Chung, C. Fox, Calculation of wave-ice interaction using the Wiener-Hopf technique. N. Z. J. Math. 31, 1–18 (2002)
R. Gayen, B.N. Mandal, A. Chakrabarti, Water-wave scattering by an ice-strip. J. Eng. Math. 53, 21–37 (2005)
S.C. Martha, S.N. Bora, Reflection and transmission coefficients for water wave scattering by a sea-bed with small undulation. ZAMM, Zeitschrift fiir Angewandte Mathematik und Mechanik 87, 314–321 (2007)
S. Zhu, Water waves within a porous medium on an undulating bed. Coast. Eng. 42, 87–101 (2001)
R. Silva, P. Salles, A. Palacio, Linear wave propagating over a rapidly varying finite porous bed. Coast. Eng. 44, 239–260 (2002)
D.V. Evans, C.M. Linton, On step approximations for water-wave problems. J. Fluid Mech. 278, 229–249 (1994)
B.N. Mandal, U. Basu, Wave diffraction by a small elevation of the bottom of an ocean with an ice-cover. Arch. Appl. Mech. 73, 812–822 (2004)
H. Mase, K. Takeba, Bragg scattering of waves over porous rippled bed, in Proceedings of the 24th ICCE’94 (1994), pp. 635–649
S.C. Martha, S.N. Bora, A. Chakrabarti, Oblique water-wave scattering by small undulation on a porous sea-bed. Appl. Ocean Res. 29, 86–90 (2007)
S. Mohapatra, S.N. Bora, Oblique water wave scattering by bottom undulation in a two-layer fluid flowing through a channel. J. Mar. Sci. Appl. 11, 276–285 (2012)
R.V. Gol’dshtein, A.V. Marchenko, The diffraction of plane gravitational waves by the edge of an ice cover. PMM USSR 53, 731–736 (1989)
P.F. Rhodes-Robinson, Fundamental singularities in the theory of water waves with surface tension. Bull. Aust. Math. Soc. 2, 317–333 (1970)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer India
About this paper
Cite this paper
Paul, S., De, S. (2015). Scattering of Water Wave by Undulating Porous Bed Topography in an Ice-Covered Ocean. In: Sarkar, S., Basu, U., De, S. (eds) Applied Mathematics. Springer Proceedings in Mathematics & Statistics, vol 146. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2547-8_26
Download citation
DOI: https://doi.org/10.1007/978-81-322-2547-8_26
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2546-1
Online ISBN: 978-81-322-2547-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)