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Unsteady flow over a submerged source with low Froude number

Published online by Cambridge University Press:  04 August 2014

CHRISTOPHER J. LUSTRI  and
S. JONATHAN CHAPMAN
CHRISTOPHER J. LUSTRI
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia E-mail: christopher.lustri@sydney.edu.au
S. JONATHAN CHAPMAN
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK
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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. Previous studies have considered linearized steady flow past a submerged source in infinite-depth fluids, in which exponential asymptotics were used to determine the behaviour of downstream longitudinal and transverse free-surface gravity waves. Here, unsteady flow past a submerged source in an infinite-depth fluid is investigated, with the free surface taken to be initially waveless. The source is taken to be weak, and the flow is linearized about the undisturbed solution. Exponential asymptotics are applied to determine the wave behaviour on the free surface in terms of the two-dimensional plan-view, in order to show how the free surface waves evolve over time and eventually tend to the steady solution.

Keywords

Free-surface potential flowsGravity wavesSingular perturbations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 5 , October 2014 , pp. 655 - 680
Copyright
Copyright © Cambridge University Press 2014 

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