Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom

Open access


A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Lamb H. (1945): Hydrodynamics. – New York: Dover.

  • [2] Stoker J.J. (1957): Water Waves the Mathematical Theory with Applications. – New York: Interscience Publishers.

  • [3] Jeffreys H. and Lapwood E.R. (1957): The reflexion of a pulse within a sphere. – Proc. Roy. Soc. A London vol.241 pp.455-479.

  • [4] Kranzer H.C. and Keller J.B. (1959): Water waves produced by explosions. – J. Appl. Phys. vol.30 pp.398–407.

  • [5] Mandal B.N. and Mukherjee S. (1989): Water waves generated at an inertial surface by an axisymmetric initial surface disturbance. – Int. J. Math. Educ. Sci. Tech. vol.20 pp.743-747.

  • [6] Maiti P. and Mandal B.N. (2005): Water waves generated due to initial axisymmetric disturbances in water with an ice-cover. – Arch. Appl. Mech. vol.74 pp.629-636.

  • [7] Martha S.C. Bora S.N. and Chakrabarti A. (2007): Oblique water wave scattering by small undulation on a porous sea bed. – Appl. Ocean. Res. vol.29 pp.86-90.

  • [8] Maiti P. and Mandal B.N. (2014): Water wave scattering by an elastic plate floating in an ocean with a porous bed. – Appl. Ocean. Res. vol.47 pp.73-84.

Journal information
Impact Factor

CiteScore 2018: 0.4

SCImago Journal Rank (SJR) 2018: 0.163
Source Normalized Impact per Paper (SNIP) 2018: 0.439

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 74 74 18
PDF Downloads 59 59 16