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A simulation-based mechanistic study of turbulent wind blowing over opposing water waves

Published online by Cambridge University Press:  27 August 2020

Tao Cao ,
Bing-Qing Deng Open the ORCID record for Bing-Qing Deng [Opens in a new window]  and
Lian Shen Open the ORCID record for Lian Shen [Opens in a new window]
Tao Cao
Affiliation:
Department of Mechanical Engineering and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55455, USA
Bing-Qing Deng
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

We perform large-eddy simulation (LES) and theoretical analysis to investigate the effects of opposing waves on overlying turbulent wind. The LES results show that opposing waves induce nearly antisymmetric vertical velocity $\tilde {w}$ in the wind on the two sides of the wave crest, while the streamwise velocity $\tilde {u}$ away from the surface and the air pressure $\tilde {p}$ seem symmetric. To study the mechanisms for the wave-induced airflow, we develop a viscous model by linearising the phase-averaged Navier–Stokes equations in the mapped computational curvilinear coordinate. To illustrate the flow dynamics, we split $\tilde {w}$ into an antisymmetric component and a symmetric component. The solution of the antisymmetric component of $\tilde {w}$ from the viscous curvilinear model agrees well with the LES results for different opposing wave conditions. According to the viscous curvilinear model, the large-magnitude antisymmetric component of $\tilde {w}$ is driven by the wave kinematics at the surface and amplified by the mean shear and viscous stress in the air, and it causes the strong symmetric components of $\tilde {u}$ and $\tilde {p}$. In contrast, the small-magnitude symmetric component of $\tilde {w}$ is forced by the antisymmetric $\tilde {w}$ through viscous and turbulent stresses near the surface, and it can be described by a further simplified inviscid curvilinear model away from the surface. It is discovered that the weak symmetric $\tilde {w}$ causes a slight asymmetry in $\tilde {u}$ and $\tilde {p}$, and generates a mean wave-coherent stress and the form drag on the wave surface. The wave attenuation rates quantified using the form drag agree with the published experiments.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A27
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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