scholarly journals New evolution equations for non-linear water waves in general bathymetry with application to steady travelling solutions in constant, but arbitrary, depth

2007 ◽  
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Non Linear ◽  
Linear Water Waves

Non-linear water waves on shearing flows

1994 ◽  
Vol 10 (2) ◽  
pp. 97-102 ◽  
Author(s):  
Chen Yaosong ◽  
Ling Guocan ◽  
Jiang Tao
Keyword(s):  
Water Waves ◽  
Non Linear ◽  
Linear Water Waves

Non-linear dispersion of water waves

1967 ◽  
Vol 27 (2) ◽  
pp. 399-412 ◽  
Author(s):  
G. B. Whitham
Keyword(s):  
Water Waves ◽  
Wave Train ◽  
Periodic Wave ◽  
Wave Number ◽  
Amplitude Wave ◽  
Linear Dispersion ◽  
Elliptic Case ◽  
Non Linear ◽  
Wave Trains ◽  
Linear Water Waves

The slow dispersion of non-linear water waves is studied by the general theory developed in an earlier paper (Whitham 1965b). The average Lagrangian is calculated from the Stokes expansion for periodic wave trains in water of arbitrary depth. This Lagrangian can be used for the various applications described in the above reference. In this paper, the crucial question of the ‘type’ of the differential equations for the wave-train parameters (local amplitude, wave-number, etc.) is established. The equations are hyperbolic or elliptic according to whetherkh0is less than or greater than 1.36, wherekis the wave-number per 2π andh0is the undisturbed depth. In the hyperbolic case, changes in the wave train propagate and the characteristic velocities give generalizations of the linear group velocity. In the elliptic case, modulations in the wave train grow exponentially and a periodic wave train will be unstable in this sense; thus, periodic wave trains on water will be unstable ifkh0> 1·36, The instability of deep-water waves,kh0> 1·36, was discovered in a different way by Benjamin (1966). The relation between the two approaches is explained.

A numerical method for non-linear water waves

1984 ◽  
Vol 12 (2) ◽  
pp. 133-143 ◽  
Author(s):  
W.K. Soh
Keyword(s):  
Numerical Method ◽  
Water Waves ◽  
Non Linear ◽  
Linear Water Waves

Research in Non-Linear Water Waves

1991 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Water Waves ◽  
Non Linear ◽  
Linear Water Waves

Applicability and limitations of highly non-linear potential flow solvers in the context of water waves

2017 ◽  
Vol 142 ◽  
pp. 233-244 ◽  
Author(s):  
Guillaume Ducrozet ◽  
Félicien Bonnefoy ◽  
Yves Perignon
Keyword(s):  
Potential Flow ◽  
Water Waves ◽  
Linear Potential ◽  
Non Linear
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