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Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield

Published online by Cambridge University Press:  30 May 2013

Di Yang ,
Charles Meneveau  and
Lian Shen
Di Yang
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, Baltimore, MD 21218, USA
Lian Shen*
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA St Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA
*
†Email address for correspondence: shen@umn.edu
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Abstract

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Wind blowing over the ocean surface can be treated as a turbulent boundary layer over a multiscale rough surface with moving roughness elements, the waves. Large-eddy simulation (LES) of such flows is challenging because LES resolves wind–wave interactions only down to the grid scale, $\Delta $, while the effects of subgrid-scale (SGS) waves on the wind need to be modelled. Usually, a surface-layer model based on the law of the wall is used; but the surface roughness has been known to depend on the local wind and wave conditions and is difficult to parameterize. In this study, a dynamic model for the SGS sea-surface roughness is developed, with the roughness corresponding to the SGS waves expressed as ${\alpha }_{w} \hspace{0.167em} { \sigma }_{\eta }^{\Delta } $. Here, ${ \sigma }_{\eta }^{\Delta } $ is the effective amplitude of the SGS waves, modelled as a weighted integral of the SGS wave spectrum based on the geometric and kinematic properties of the waves for which five candidate expressions are examined. Moreover, ${\alpha }_{w} $ is an unknown dimensionless model coefficient determined dynamically based on the first-principles constraint that the total surface drag force or average surface stress must be independent of the LES filter scale $\Delta $. The feasibility and consistency of the dynamic sea-surface roughness models are assessed by a priori tests using data from high-resolution LES with near-surface resolution, appropriately filtered. Also, these data are used for a posteriori tests of the dynamic sea-surface roughness models in LES with near-surface modelling. It is found that the dynamic modelling approach can successfully capture the effects of SGS waves on the wind turbulence without ad hoc prescription of the model parameter ${\alpha }_{w} $. Also, for ${ \sigma }_{\eta }^{\Delta } $, a model based on the kinematics of wind–wave relative motion achieves the best performance among the five candidate models.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 62 - 99
Copyright
©2013 Cambridge University Press 

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