Faculty Publications

Title

Capillary-gravity waves and the Navier-Stokes equation

Document Type

Article

Journal/Book/Conference Title

European Journal of Physics

Volume

22

Issue

6

First Page

587

Last Page

593

Abstract

Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation.

Original Publication Date

11-1-2001

DOI of published version

10.1088/0143-0807/22/6/303

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