an:06286115
Zbl 1302.76032
Laouar, A.; Guerziz, A.; Boughaba, S.
Numerical simulation for a free surface of a long gravity wave
EN
Ilirias J. Math. 2, No. 1, 1-10 (2013).
00331819
2013
j
76B15 74J15 35A15
free surface; long gravity wave; shallow water theory
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 Poincar??'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.