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Ship generated mini-tsunamis

Published online by Cambridge University Press:  03 March 2017

John Grue Open the ORCID record for John Grue [Opens in a new window]
John Grue*
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, Oslo, Norway
*
†Email address for correspondence: johng@math.uio.no
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Abstract

Very long waves are generated when a ship moves across an appreciable depth change $\unicode[STIX]{x0394}h$ comparable to the average and relatively shallow water depth $h$ at the location, with $\unicode[STIX]{x0394}h/h\simeq 1$. The phenomenon is new and the waves were recently observed in the Oslofjord in Norway. The 0.5–1 km long waves, extending across the 2–3 km wide fjord, are observed as run-ups and run-downs along the shore, with periods of 30–60 s, where a wave height up to 1.4 m has been measured. The waves travelling with the shallow water speed, found ahead of the ships moving at subcritical depth Froude number, behave like a mini-tsunami. A qualitative explanation of the linear generation mechanism is provided by an asymptotic analysis, valid for $\unicode[STIX]{x0394}h/h\ll 1$ and long waves, expressing the generation in terms of a pressure impulse at the depth change. Complementary fully dispersive calculations for $\unicode[STIX]{x0394}h/h\simeq 1$ document symmetries of the waves at positive or negative $\unicode[STIX]{x0394}h$. The wave height grows with the ship speed $U$ according to $U^{n}$ with $n$ in the range 3–4, for $\unicode[STIX]{x0394}h/h\simeq 1$, while the growth in $U$ is only very weak for $\unicode[STIX]{x0394}h/h\ll 1$ (the asymptotics). Calculations show good agreement with observations.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Topographic effects Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 816 , 10 April 2017 , pp. 142 - 166
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Copyright
© 2017 Cambridge University Press 

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