Differential Equations and Nonlinear Mechanics
Volume 2008 (2008), Article ID 135982, 11 pages
Research Article

Numerical Simulation of the Field Velocities and Local Disturbances of a Long Gravity Wave Passing above an Immersed Vertical Barrier

Laouar Abdelhamid1 and Guerziz Allaoua2

1Department of Mathematics, University of Annaba, P.O. Box 12, 23000 Annaba, Algeria
2Department of Physics, University of Annaba, P.O. Box 12, 23000 Annaba, Algeria

Received 20 October 2007; Revised 21 July 2008; Accepted 26 August 2008

Academic Editor: Roger Grimshaw

Copyright © 2008 Laouar Abdelhamid and Guerziz Allaoua. 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.


This work is interested in the study of the passage of a long gravity wave above an immersed vertical barrier. The latter is placed at a right angle in the middle of the occupied fluid domain which is limited vertically by both a free surface and an impermeable horizontal bottom. We want to determine the field velocity and the local disturbances in the vicinity of the barrier. For this, we use the generalized theory of shallow water and complex variables method. For illustration, we consider a solitary wave as an emitted long wave.