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Steady gravity waves due to a submerged source

Published online by Cambridge University Press:  12 September 2013

Christopher J. Lustri  and
S. Jonathan Chapman
Christopher J. Lustri*
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
S. Jonathan Chapman
Affiliation:
Oxford Center for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK
*
†Email address for correspondence: c.lustri@maths.usyd.edu.au
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Abstract

In the low-Froude-number limit, free-surface gravity waves caused by flow past a submerged obstacle have amplitude that is exponentially small. Consequently, these cannot be represented using an asymptotic series expansion. Steady linearized flow past a submerged source is considered, and exponential asymptotic methods are applied to determine the behaviour of the free-surface gravity waves. The free surface is found to contain longitudinal and transverse waves that switch on rapidly across curves known as Stokes lines on the free surface. The longitudinal waves are present everywhere downstream of the singularity, while the transverse waves are restricted to two downstream wedges. As the depth of the source approaches the surface, the familiar Kelvin-wedge wave behaviour is recovered.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 732 , 10 October 2013 , pp. 660 - 686
Copyright
©2013 Cambridge University Press 

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