Semi-discrete and discrete gradient for non linear water wave problems

2006 ◽  
pp. 297-310 ◽  
Author(s):  
M. Souli ◽  
J. P. Zolesio
Keyword(s):  
Water Wave ◽  
Discrete Gradient ◽  
Non Linear ◽  
Wave Problems

Unsteady non-linear waves in sloping channels

1958 ◽  
Vol 247 (1249) ◽  
pp. 186-198 ◽  
Keyword(s):  
Exact Solution ◽  
Water Wave ◽  
Legendre Function ◽  
Elliptic Integral ◽  
Vertical Wall ◽  
Auxiliary Function ◽  
Level Line ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Non Linear

It is shown in general that the exact solution to every non-degenerate unsteady water-wave problem in a straight channel inclined at arbitrary slope, governed by the non-linear hydraulic equations, can be obtained in terms of the complete elliptic integral of the second kind, E . By means of a non-Newtonian reference frame, every such wave problem for a sloping channel can be replaced by an associated problem for a horizontal channel. For the latter, the partial differential equations become reducible and thus permit hodograph inversion. The Riemann integration method for the resulting Euler-Poisson equation yields an auxiliary function for these hydraulic problems which is transformable into a Legendre function and then into the elliptic integral. In particular, the procedure is applied to obtain the exact solution for the water wave in a sloping channel produced by sudden release of the triangular wedge of water (the reservoir) initially at rest behind a vertical wall. The behaviour of the solution is exhibited for convenience in two level-line charts, and representative wave profiles and velocity distributions are presented.

An Acoustic Model for the Experimental Study of Water‐Wave Problems

1971 ◽  
Vol 50 (6A) ◽  
pp. 1443-1446 ◽  
Author(s):  
R. P. Shaw ◽  
A. Parvulescu
Keyword(s):  
Experimental Study ◽  
Water Wave ◽  
Acoustic Model ◽  
Wave Problems

Method of Analyses for Two-Dimensional Water Wave Problems

1977 ◽  
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Akinori Yoshida
Keyword(s):  
Water Wave ◽  
Two Dimensional ◽  
Wave Problems
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