Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom
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...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2019-08-01
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| Series: | International Journal of Applied Mechanics and Engineering |
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| Online Access: | https://www.ijame-poland.com/Generation-of-Surface-Waves-Due-to-Initial-Axisymmetric-Surface-Disturbance-in-Water,166909,0,2.html |
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| author | P. Kundu B.N. Mandal |
| author_facet | P. Kundu B.N. Mandal |
| author_sort | P. Kundu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:33:38Z |
| format | Article |
| id | doaj.art-9651de78a60c45e08f368c25fcaaf52c |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:33:38Z |
| publishDate | 2019-08-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-9651de78a60c45e08f368c25fcaaf52c2023-08-08T15:01:28ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032019-08-0124362564410.2478/ijame-2019-0039166909Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous BottomP. Kundu0B.N. Mandal1Department of Mathematics, Jadavpur University, Kolkata-, 700032, IndiaPhysics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T Road, Kolkata-, 700108, IndiaA 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.https://www.ijame-poland.com/Generation-of-Surface-Waves-Due-to-Initial-Axisymmetric-Surface-Disturbance-in-Water,166909,0,2.htmlaxisymmetric surface disturbanceporous bottomlaplace and hankel transformmethod of stationary phasefree surface depression |
| spellingShingle | P. Kundu B.N. Mandal Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom International Journal of Applied Mechanics and Engineering axisymmetric surface disturbance porous bottom laplace and hankel transform method of stationary phase free surface depression |
| title | Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom |
| title_full | Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom |
| title_fullStr | Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom |
| title_full_unstemmed | Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom |
| title_short | Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom |
| title_sort | generation of surface waves due to initial axisymmetric surface disturbance in water with a porous bottom |
| topic | axisymmetric surface disturbance porous bottom laplace and hankel transform method of stationary phase free surface depression |
| url | https://www.ijame-poland.com/Generation-of-Surface-Waves-Due-to-Initial-Axisymmetric-Surface-Disturbance-in-Water,166909,0,2.html |
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