Saint-Venant, A.J.C. (1871) Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et a l’introduction de marées dans leurs lits. Comptes Rendus des Séances de Académie des Sciences, 73, 147, 237.

has been cited by the following article:

• TITLE: Dimension-Reduced Model for Deep-Water Waves

  AUTHORS: Michael Bestehorn, Peder A. Tyvand, Thomas Michelitsch

  KEYWORDS: Hydrodynamics, Ocean Waves, Deep-Water Waves, Numerical Solutions, Fractal Derivatives

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.1, January 15, 2019

  ABSTRACT: Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.