A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes' theory

David Needham; J Billingham

doi:10.1098/rspa.2008.0145

A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes' theory

David Needham, J Billingham

Mathematics

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Abstract

In this paper, we develop a theory based on local asymptotic coordinate expansions for the unsteady propagation of a corner point on the constant-pressure free surface bounding an incompressible inviscid fluid in irrotational motion under the action of gravity. This generalizes the result of Stokes and Michell relating to the horizontal propagation of a corner at constant speed.

Original language	English
Pages (from-to)	165-173
Number of pages	9
Journal	Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Volume	465
Issue number	2101
Early online date	16 Sept 2008
DOIs	https://doi.org/10.1098/rspa.2008.0145
Publication status	Published - 8 Jan 2009

Keywords

Stokes' 120 degrees corner flow
inviscid irrotational free surface flow
Stokes wave

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10.1098/rspa.2008.0145

Cite this

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abstract = "In this paper, we develop a theory based on local asymptotic coordinate expansions for the unsteady propagation of a corner point on the constant-pressure free surface bounding an incompressible inviscid fluid in irrotational motion under the action of gravity. This generalizes the result of Stokes and Michell relating to the horizontal propagation of a corner at constant speed.",

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T1 - A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes' theory

AU - Needham, David

AU - Billingham, J

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Y1 - 2009/1/8

N2 - In this paper, we develop a theory based on local asymptotic coordinate expansions for the unsteady propagation of a corner point on the constant-pressure free surface bounding an incompressible inviscid fluid in irrotational motion under the action of gravity. This generalizes the result of Stokes and Michell relating to the horizontal propagation of a corner at constant speed.

AB - In this paper, we develop a theory based on local asymptotic coordinate expansions for the unsteady propagation of a corner point on the constant-pressure free surface bounding an incompressible inviscid fluid in irrotational motion under the action of gravity. This generalizes the result of Stokes and Michell relating to the horizontal propagation of a corner at constant speed.

KW - Stokes' 120 degrees corner flow

KW - inviscid irrotational free surface flow

KW - Stokes wave

U2 - 10.1098/rspa.2008.0145

DO - 10.1098/rspa.2008.0145

M3 - Article

SN - 1471-2946

VL - 465

SP - 165

EP - 173

JO - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

JF - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

IS - 2101

ER -

A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes' theory

Abstract

Keywords

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