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Linear stern waves in finite depth channels

McCue, Scott W. & Stump, David M. (2000) Linear stern waves in finite depth channels. Quarterly Journal of Mechanics and Applied Mathematics, 53(4), pp. 629-643.

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Abstract

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Impact and interest:

7 citations in Scopus
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7 citations in Web of Science®

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27 since deposited on 14 Feb 2011
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ID Code: 40050
Item Type: Journal Article
Keywords: stern waves, free surface flows, Wiener-Hopf technique, semi-infinite plate
DOI: 10.1093/qjmam/53.4.629
ISSN: 1464-3855
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Approximation Theory and Asymptotic Methods (010201)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2000 Oxford University Press
Deposited On: 15 Feb 2011 09:54
Last Modified: 30 Jan 2013 08:36

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