International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 399-404
Surface water waves due to an oscillatory wavemaker in the presence of surface tension
1Physical and Earth Sciences Division, Indian Statistical Institute, 203, B.T. Road, Calcutta 700035, USA
2Calcutta Mathematical Society, 92, A.P.C. Road, Calcutta 700009, India
Received 28 March 1990
Copyright © 1992 B. N. Mandal and S. Banerjea. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The initial value problem of generation of surface water waves by a harmonically oscillating plane vertical wavemaker in an infinite incompressible fluid under the action of gravity and surface tension is investigated. In the asymptotic evaluation of the free surface depression for large time and distance, the contribution to the integral by stationary phase method gives rise to transient component of the free surface depression while the contribution from the poles give rise to steady state component. It is observed that the presence of surface tension sometimes changes the qualitative nature of the transient component of free surface depression.