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On the physical mechanism of front–back asymmetry of non-breaking gravity–capillary waves

Published online by Cambridge University Press:  13 November 2020

Alexander Dosaev Open the ORCID record for Alexander Dosaev [Opens in a new window] ,
Yuliya I. Troitskaya Open the ORCID record for Yuliya I. Troitskaya [Opens in a new window]  and
Victor I. Shrira Open the ORCID record for Victor I. Shrira [Opens in a new window]
Alexander Dosaev
Affiliation:
Department of Nonlinear Geophysical Processes, Institute of Applied Physics, 46 Ulyanov Street, Nizhny Novgorod603950, Russia
Yuliya I. Troitskaya
Affiliation:
Department of Nonlinear Geophysical Processes, Institute of Applied Physics, 46 Ulyanov Street, Nizhny Novgorod603950, Russia
Victor I. Shrira*
Affiliation:
School of Computing and Mathematics, Keele University, KeeleST5 5BG, UK
*
†Email address for correspondence: v.i.shrira@keele.ac.uk
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Abstract

In nature, the wind waves of the gravity–capillary range are noticeably skewed forward. The salient feature of such waves is a characteristic pattern of capillary ripples on their crests. The train of these ‘parasitic capillaries’ is not symmetric with respect to the crest, it is localised on the front slope and decays towards the trough. Although understanding the gravity–capillary waves front–back asymmetry is important for remote sensing and, potentially, for wave–wind interaction, the physical mechanisms causing this asymmetry have not been identified. Here, we address this gap by extensive numerical simulations of the Euler equations employing the method of conformal mapping for two-dimensional potential flow and taking into account wave generation by wind and dissipation due to molecular viscosity. On examining the role of various factors contributing to the wave profile front–back asymmetry: wind forcing, viscous stresses and the Reynolds stresses caused by ripples, we found, in the absence of wave breaking, the latter to be by far the most important. It is the lopsided ripple distribution which leads to the noticeable fore–aft asymmetry of the mean wave profile. We also found how the asymmetry depends on wavelength, steepness, wind, viscosity and surface tension. The results of the model are discussed in the context of the available experimental data on asymmetry of gravity–capillary waves in both the breaking and non-breaking regimes. A reasonable agreement of the model with the data has been found for the regime without breaking or microbreaking.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Wind-wave interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A11
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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