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Crest speeds of unsteady surface water waves

Published online by Cambridge University Press:  17 July 2020

Francesco Fedele Open the ORCID record for Francesco Fedele [Opens in a new window] ,
Michael L. Banner Open the ORCID record for Michael L. Banner [Opens in a new window]  and
Xavier Barthelemy Open the ORCID record for Xavier Barthelemy [Opens in a new window]
Francesco Fedele*
Affiliation:
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Michael L. Banner
Affiliation:
School of Mathematics and Statistics, UNSW Australia, Sydney, NSW2052, Australia
Xavier Barthelemy
Affiliation:
School of Mathematics and Statistics, UNSW Australia, Sydney, NSW2052, Australia Water Research Laboratory, School of Civil and Environmental Engineering, UNSW Australia, Sydney, NSW2052, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Intuitively, crest speeds of water waves are assumed to match their phase speeds. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the generic behaviour of crest speeds of linear to highly nonlinear unsteady waves. While our major focus is on gravity waves where a generic crest slowdown occurs cyclically, results for capillary-dominated waves are also discussed, for which crests cyclically speed up. This curious phenomenon arises when the theoretical constraint of steadiness is relaxed, allowing waves to change their form, or shape. In particular, a kinematic analysis of both simulated and observed open-ocean gravity waves reveals a forward-to-backward leaning cycle for each individual crest within a wave group. This is clearly manifest during the focusing of dominant wave groups essentially due to the dispersive nature of waves. It occurs routinely for focusing linear (vanishingly small steepness) wave groups, and it is enhanced as the wave spectrum broadens. It is found to be relatively insensitive to the degree of phase coherence and focusing of wave groups. The nonlinear nature of waves limits the crest slowdown. This reduces when gravity waves become less dispersive, either as they steepen or as they propagate over finite water depths. This is demonstrated by numerical simulations of the unsteady evolution of two- and three-dimensional dispersive gravity wave packets in both deep and intermediate water depths, and by open-ocean space–time measurements.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A5
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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