Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom
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Department of Mathematics, Jadavpur University, Kolkata-, 700032, India
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T Road, Kolkata-, 700108, India
Online publication date: 2019-08-09
Publication date: 2019-09-01
International Journal of Applied Mechanics and Engineering 2019;24(3):625-644
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.
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