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Wave breaking and jet formation on axisymmetric surface gravity waves

Published online by Cambridge University Press:  25 January 2022

M.L. McAllister Open the ORCID record for M.L. McAllister [Opens in a new window] ,
S. Draycott Open the ORCID record for S. Draycott [Opens in a new window] ,
T. Davey Open the ORCID record for T. Davey [Opens in a new window] ,
Y. Yang ,
T.A.A. Adcock Open the ORCID record for T.A.A. Adcock [Opens in a new window] ,
S. Liao Open the ORCID record for S. Liao [Opens in a new window]  and
T.S. van den Bremer Open the ORCID record for T.S. van den Bremer [Opens in a new window]
M.L. McAllister*
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
S. Draycott
Affiliation:
Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M60 1QD, UK
T. Davey
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, UK
Y. Yang
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
T.A.A. Adcock
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
S. Liao
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China State Key Lab of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
T.S. van den Bremer
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CD Delft, The Netherlands
*
†Email address for correspondence: mark.mcallister@eng.ox.ac.uk
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Abstract

Axisymmetric standing waves occur across a wide range of free surface flows. When these waves reach a critical height (steepness), wave breaking and jet formation occur. For travelling surface gravity waves, wave breaking is generally considered to limit wave height and reversible wave motion. In the ocean, the behaviour of directionally spread waves lies between the limits of purely travelling (two dimensions) and axisymmetric (three dimensions). Hence, understanding wave breaking and jet formation on axisymmetric surface gravity waves is an important step in understanding extreme and breaking waves in the ocean. We examine an example of axisymmetric wave breaking and jet formation colloquially known as the ‘spike wave’, created in the FloWave circular wave tank at the University of Edinburgh, UK. We generate this spike wave with maximum crest amplitudes of 0.15–6.0 m (0.024–0.98 when made non-dimensional by characteristic radius), with wave breaking occurring for crest amplitudes greater than 1.0 m (0.16 non-dimensionalised). Unlike two-dimensional travelling waves, wave breaking does not limit maximum crest amplitude, and our measurements approximately follow the jet height scaling proposed by Ghabache et al. (J. Fluid Mech., vol. 761, 2014, pp. 206–219) for cavity collapse. The spike wave is predominantly created by linear dispersive focusing. A trough forms, then collapses producing a jet, which is sensitive to the trough's shape. The evolution of the jets that form in our experiments is predicted well by the hyperbolic jet model proposed by Longuet–Higgins (J. Fluid Mech., vol. 127, 1983, pp. 103–121), previously applied to jets forming on bubbles.

JFM classification

Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Surface gravity waves

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JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A5
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© The Author(s), 2022. Published by Cambridge University Press

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McAllister et al. supplementary movie 1

Video of Exp. 75, played at a reduced frame rate of 25 fps.

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McAllister et al. supplementary movie 2

Video of Exp. 70, played at a reduced frame rate of 25 fps.

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McAllister et al. supplementary movie 3

Video of Exp. 60, played at a reduced frame rate of 25 fps.

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McAllister et al. supplementary movie 4

Video of Exp. 50, played at a reduced frame rate of 25 fps.

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McAllister et al. supplementary movie 5

Video of Exp. 60, played at a reduced frame rate of 25 fps.

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McAllister et al. supplementary movie 6

Video of Exp. 40, played at a reduced frame rate of 25 fps.

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McAllister et al. supplementary movie 7

Video of Exp. 50 with sound, played once at full speed then at 10% of full speed.

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