Dimension-Reduced Model for Deep-Water Waves - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.1, January 2019

Journal of Applied Mathematics and Physics

Volume 7, Issue 1 (January 2019)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

Dimension-Reduced Model for Deep-Water Waves ()

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Download as PDF (Size: 5831KB) PP. 72-92

DOI: 10.4236/jamp.2019.71007 654 Downloads 1,324 Views Citations

Author(s)

Michael Bestehorn¹, Peder A. Tyvand², Thomas Michelitsch³

Affiliation(s)

¹Department of Physics, Brandenburg University of Technology, Cottbus, Germany.
²Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway.
³CNRS, Institut Jean le Rond d’Alembert, Sorbonne Université, Paris, France.

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.

KEYWORDS

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

Share and Cite:

Bestehorn, M. , Tyvand, P. and Michelitsch, T. (2019) Dimension-Reduced Model for Deep-Water Waves. Journal of Applied Mathematics and Physics, 7, 72-92. doi: 10.4236/jamp.2019.71007.

Cited by

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	Journal of Fluid Mechanics, 2021

[2]	A nonlinear impulsive Cauchy–Poisson problem. Part 1. Eulerian description
	2020

[3]	Rayleigh–Taylor and Kelvin–Helmholtz instability studied in the frame of a dimension-reduced model
	2020

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