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A formulation of convective entrainment in terms of mixing efficiency

Published online by Cambridge University Press:  21 May 2007

C. CHEMEL  and
C. STAQUET
C. CHEMEL*
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels, CNRS/UJF/INPG BP 53, 38041Grenoble Cedex 9, France
C. STAQUET
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels, CNRS/UJF/INPG BP 53, 38041Grenoble Cedex 9, France
*
†Author to whom correspondence should be addressed: c.chemel@herts.ac.uk.
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Abstract

The entrainment across a stably stratified interface forced by convective motions is discussed in the light of the mixing efficiency of the entrainment process. The context is the convectively driven atmospheric boundary layer and we focus on the regime of equilibrium entrainment, i.e. when the boundary-layer evolution is in a quasi-steady state. The entrainment law is classically based on the ratio R of the negative of the heat flux at the interface to the heat flux at the ground surface. We propose a parameterization for R that involves the mixing efficiency and the thickness of the interface, which matches well the direct computation of R from a high-resolution large-eddy simulation. This result enables us to derive modified expressions for the classical entrainment laws (the so-called zero- and first-order models) as a function of the mixing efficiency. We show that, when the thickness of the interface is ignored (zero-order model), the scaling factor A in the entrainment law is the flux Richardson number. This parameterization of A is further improved when the thickness of the interface is considered (first-order model), as shown by the direct computation of A from the large-eddy simulation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 580 , 10 June 2007 , pp. 169 - 178
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

Present address: Centre for Atmospheric Atmospheric and Instrumentation Research, University of Hertfordshire, College Lane Campus, Hatfield, Herts AL10 9AB, UK.

References

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