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Kelvin wake pattern at small Froude numbers

Published online by Cambridge University Press:  31 March 2021

Ravindra Pethiyagoda Open the ORCID record for Ravindra Pethiyagoda [Opens in a new window] ,
Timothy J. Moroney Open the ORCID record for Timothy J. Moroney [Opens in a new window] ,
Christopher J. Lustri Open the ORCID record for Christopher J. Lustri [Opens in a new window]  and
Scott W. McCue Open the ORCID record for Scott W. McCue [Opens in a new window]
Ravindra Pethiyagoda
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
Timothy J. Moroney
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
Christopher J. Lustri
Affiliation:
Department of Mathematics, Macquarie University, Sydney NSW 2109, Australia
Scott W. McCue*
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia
*
†Email address for correspondence: scott.mccue@qut.edu.au
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Abstract

The surface gravity wave pattern that forms behind a steadily moving disturbance is well known to comprise divergent waves and transverse waves, contained within a distinctive $V$-shaped wake. In this paper, we are concerned with a theoretical study of the limit of a slow-moving disturbance (small Froude numbers) in the absence of surface tension, for which the wake is dominated by transverse waves. Three configurations are considered: flow past a submerged source singularity, a submerged doublet and a pressure distribution applied to the surface. We treat the linearised version of these problems and use the method of stationary phase and exponential asymptotics to demonstrate that the apparent wake angle is less than the classical Kelvin angle and to quantify the decrease in apparent wake angle as the Froude number decreases. These results complement a number of recent studies for sufficiently fast-moving disturbances (large Froude numbers) where the apparent wake angle has been also shown to be less than the classical Kelvin angle. As well as shedding light on the issue of apparent wake angle, we also study the fully nonlinear problems for our three configurations under various limits to demonstrate the unique and interesting features of Kelvin wake patterns at small Froude numbers.

JFM classification

Waves/Free-surface Flows: Surface gravity waves

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JFM Papers
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Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A126
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© The Author(s), 2021. Published by Cambridge University Press

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References

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