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Three-dimensional capillary waves due to a submerged source with small surface tension

Published online by Cambridge University Press:  28 January 2019

Christopher J. Lustri Open the ORCID record for Christopher J. Lustri [Opens in a new window] ,
Ravindra Pethiyagoda Open the ORCID record for Ravindra Pethiyagoda [Opens in a new window]  and
S. Jonathan Chapman Open the ORCID record for S. Jonathan Chapman [Opens in a new window]
Christopher J. Lustri*
Affiliation:
Department of Mathematics and Statistics, Macquarie University, Sydney NSW 2109, Australia
Ravindra Pethiyagoda
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
S. Jonathan Chapman
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK
*
†Email address for correspondence: [email protected]
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Abstract

Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension, and are determined using the theory of exponential asymptotics. In the steady problem, capillary waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions are compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential asymptotics is applied to show how the capillary waves evolve over time, and eventually tend to the steady solution.

JFM classification

Waves/Free-surface Flows: Capillary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 670 - 701
Copyright
© 2019 Cambridge University Press 

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