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.