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Direct simulation of surface roughness signature of internal wave with deterministic energy-conservative model

Published online by Cambridge University Press:  24 March 2020

Xuanting Hao Open the ORCID record for Xuanting Hao [Opens in a new window]  and
Lian Shen Open the ORCID record for Lian Shen [Opens in a new window]
Xuanting Hao
Affiliation:
Department of Mechanical Engineering, and St. Anthony Falls Laboratory,University of Minnesota, Minneapolis, MN55455, USA
Lian Shen*
Affiliation:
Department of Mechanical Engineering, and St. Anthony Falls Laboratory,University of Minnesota, Minneapolis, MN55455, USA
*
†Email address for correspondence: shen@umn.edu
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Abstract

In this simulation-based study, we investigate the surface roughness signature induced by internal solitary waves in oceans. We present the first-ever effort to directly capture the surface roughness signature with a deterministic two-layer model to avoid the singularity encountered in the traditional wave–current interaction theory. By capturing over four million wave components, the simulation resolves the surface wave and internal wave dynamics simultaneously. The surface signature characterized by a rough region followed by a smooth region travelling with an internal wave is quantified by the local wave geometry variation and the wave energy change. The surface wave dynamics are analysed in the wavenumber–frequency slope spectrum calculated in the frame moving with the internal wave. The asymmetric behaviours of right-moving and left-moving surface waves are found to contribute to the surface signature formation. Our results show that the formation of the surface signature is essentially an energy-conservative process and justify the use of the wave-phase-resolved two-layer model.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Solitary waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , R3
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Supplementary material: PDF

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Supplementary data
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Hao and Shen supplementary movie 1

Evolution of the surface wave field showing the smooth and rough region
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