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Spectrograms of ship wakes: identifying linear and nonlinear wave signals

Published online by Cambridge University Press:  06 December 2016

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

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real-world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high-speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time–frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher-order effects in a spectrogram and, while the high-speed ferry data are very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high-speed ferry spectrograms and linear theory by accounting for ship acceleration.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Wakes/Jets: Wakes Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , pp. 189 - 209
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Copyright
© 2016 Cambridge University Press 

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