Numerical simulation for a free surface of a long gravity wave. (English) Zbl 1302.76032

Laouar, A.; Guerziz, A.; Boughaba, S.

Ilirias J. Math. 2, No. 1, 1-10 (2013).

Summary: This paper deals with the study of a long gravity wave profile in a bidimensional rectangular basin, and the aim of this work consists in determining a free surface equation of gravity wave. The equations of motion of such a problem with its boundaries conditions are reduced to a system of nonlinear equations. The applying shallow water theory helps to solve the system and the solution is expanded asymptotically in terms of Poincaré’s parameter \(\varepsilon\). The approximating with respect to the parameter \(\varepsilon\) at the first, second and three orders, the problem is transformed into a wave equation. A numerical example is given to support the theory.

MSC:

76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74J15	Surface waves in solid mechanics
35A15	Variational methods applied to PDEs

Keywords:

free surface; long gravity wave; shallow water theory