|Table of Contents|

 Smrutiranjan Mohapatra.Scattering of Oblique Surface Waves by the Edge of Small Deformation on a Porous Ocean Bed[J].Journal of Marine Science and Application,2015,(2):156-162.[doi:10.1007/s11804-015-1298-6]
Click and Copy

Scattering of Oblique Surface Waves by the Edge of Small Deformation on a Porous Ocean Bed


Scattering of Oblique Surface Waves by the Edge of Small Deformation on a Porous Ocean Bed
Smrutiranjan Mohapatra
Smrutiranjan Mohapatra
Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, India
oblique waves bottom deformation porous bed Green’s function perturbation technique reflection coefficient transmission coefficient scattering
The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green’s integral theorem with the introduction of appropriate Green’s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.


Chamberlain PG, Porter D (1995). The modified mild-slope equations. Journal of Fluid Mechanics, 291, 393-407.
    DOI: 10.1017/S0022112095002758
Davies AG (1982). The reflection of wave energy by undulations of the sea bed. Dynamics of Atmosphere and Oceans, 6, 207-232.
Davies AG, Heathershaw AD (1984). Surface wave propagation over sinusoidally varying topography. Journal of Fluid Mechanics, 144, 419-443.
    DOI: 10.1017/S0022112084001671
Gu Z, Wang H (1991). Gravity waves over porous bottoms. Coastal Engineering, 15, 497-524.
Jeng DS (2001). Wave dispersion equation in a porous seabed. Coastal Engineering, 28, 1585-1599.
    DOI: 10.1016/S0029-8018(00)00068-8
Kirby JT (1986). A general wave equation for waves over rippled beds. Journal of Fluid Mechanics, 162, 171-186.
    DOI: 10.1017/S0022112086001994
Mandal BN, Basu U (1990). A note on oblique water-wave diffraction by a cylindrical deformation of the bottom in the presence of surface tension. Archive of Mechanics, 42, 723-727.
Martha SC, Bora SN (2007). Oblique surface wave propagation over a small undulation on the bottom of an ocean. Geophysical and Astrophysical Fluid Dynamics, 101, 65-80.
    DOI: 10.1080/03091920701208186
Martha SC, Bora SN, Chakrabarti A (2007). Oblique water-wave scattering by small undulation on a porous sea-bed. Applied Ocean Research, 29, 86-90.
    DOI: 10.1016/j.apor.2007.07.001
Mohapatra S (2014). Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean with ice-cover. Journal of Marine Science and Application, 13, 167-172.
    DOI: 10.1007/s11804-014-1241-2
Mei CC (1985). Resonant reflection of surface water waves by periodic sandbars. Journal of Fluid Mechanics, 152, 315-335.
    DOI: 10.1017/S0022112085000714
Miles JW (1981). Oblique surface wave diffraction by a cylindrical obstacle. Dynamics of Atmosphere and Oceans, 6, 121-123.
Porter R, Porter D (2003). Scattered and free waves over periodic beds. Journal of Fluid Mechanics, 483, 129-163.
    DOI: 10.1017/S0022112003004208
Silva R, Salles P, Palacio A (2002). Linear wave propagating over a rapidly varying finite porous bed. Coastal Engineering, 44, 239-260.
    DOI: 10.1016/S0378-3839(01)00035-7
Staziker DJ, Porter D, Stirling DSG (1996). The scattering of surface waves by local bed elevations. Applied Ocean Research, 18, 283-291.
Zhu S (2001). Water waves within a porous medium on an undulating bed. Coastal Engineering, 42, 87-101.
    DOI: 10.1016/S0378-3839(00)00050-8


Received date: 2014-08-18      Accepted date: 2014-11-17
Corresponding author: Smrutiranjan Mohapatra      E-mail:smrutiranjan.m@gmail.com
Last Update: 2016-06-23