Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-20T10:18:15.361Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected].
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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

References

REFERENCES

Betts, A. K. 1974 Reply to comment on the paper ‘non-precipitating cumulus convection and its parameterization’. Q. J. R. Met. Soc. 100, 469–471.Google Scholar
Caldwell, P., Bretherton, C. S. & Wood, R. 2005 Mixed-layer budget analysis of the diurnal cycle of entrainment in Southeast Pacific stratocumulus. J. Atmos. Sci. 62, 3775–3791.CrossRefGoogle Scholar
Chemel, C., Staquet, C. & Chollet, J.-P. 2007 Eulerian- and Lagrangian-based estimates of convective entrainment rate from large-eddy simulation. J. Atmos. Sci. (submitted).Google Scholar
Clarke, R. H., Dyer, A. J., Brook, R. R., Reid, D. G. & Troup, A. J. 1971 The Wangara experiment: Boundary layer data. Tech. Paper 19. CSIRO Atmospheric Research, Aspendale, Australia.Google Scholar
Conzemius, R. & Fedorovich, E. 2006 Dynamics of sheared convective boundary layer entrainment. Part I: methodological background and large-eddy simulations. J. Atmos. Sci. 63, 1151–1178.CrossRefGoogle Scholar
Deardorff, J. W., Willis, G. E. & Stockton, B. H. 1980 Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech. 100, 41–64.CrossRefGoogle Scholar
Fedorovich, E., Conzemius, R. & Mironov, D. 2004 Convective entrainment into a shear-free, linearly stratified atmosphere: bulk models reevaluated through large eddy simulations. J. Atmos. Sci. 61, 281–295.2.0.CO;2>CrossRefGoogle Scholar
Fedorovich, E. E. & Mironov, D. V. 1995 A model for a shear-free convective boundary layer with parameterized capping inversion structure. J. Atmos. Sci. 52, 83–95.2.0.CO;2>CrossRefGoogle Scholar
Fernando, H. J. S. 1991 Turbulent mixing in stratified fluids. Anuu. Rev. Fluid Mech. 23, 455–493.CrossRefGoogle Scholar
Hopfinger, E. J. 1987 Turbulence in stratified fluids: a review. J. Geophys. Res. 92, 5287–5303.Google Scholar
Lilly, D. K. 1968 Models of cloud-topped mixed layers under a strong inversion. Q. J. R. Met. Soc. 94, 292–309.CrossRefGoogle Scholar
Lilly, D. K. 2002 Entrainment into mixed layers. Part I: sharp-edged and smoothed tops. J. Atmos. Sci. 59, 3340–3352.2.0.CO;2>CrossRefGoogle Scholar
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3–23.CrossRefGoogle Scholar
Lorenz, E. N. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7, 157–167.CrossRefGoogle Scholar
Manins, P. C. & Turner, J. S. 1978 The relation between the flux ratio and energy ratio in convectively mixed layers. Q. J. R. Met. Soc. 104, 39–44.CrossRefGoogle Scholar
McEwan, A. D. 1983 Internal mixing in stratified fluids. J. Fluid Mech. 128, 59–80.CrossRefGoogle Scholar
Moum, J. N. & Caldwell, D. R. 1995 Turbulence and mixing in the ocean. Rev. Geophys. 33, 1385–1394.Google Scholar
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Fluid Dyn. 3, 321–345.CrossRefGoogle Scholar
Otte, M. J. & Wyngaard, J. C. 2001 Stably stratified interfacial-layer turbulence from large-eddy simulation. J. Atmos. Sci. 58, 3424–3442.2.0.CO;2>CrossRefGoogle Scholar
Staquet, C. 2000 Mixing in a stably stratified shear layer: two- and three-dimensional numerical experiments. Fluid Dyn. Res. 27, 367–404.CrossRefGoogle Scholar
Stevens, B., Bell, J. B., Almgren, A. S., Beckner, V. E. & Rendleman, C. A. 2000 Small-scale processes and entrainment in a stratocumulus marine boundary layer. J. Atmos. Sci. 57, 567–581.2.0.CO;2>CrossRefGoogle Scholar
Stevens, B. & Lenschow, D. H. 2001 Observations, experiments, and large eddy simulation. Bull. Am. Met. Soc. 82, 283–294.2.3.CO;2>CrossRefGoogle Scholar
Stull, R. B. 1976 The energetics of entrainment across a density interface. J. Atmos. Sci. 33, 1260–1267.Google Scholar
Sullivan, P. P., Moeng, C.-H., Stevens, B., Lenschow, D. H. & Mayor, S. D. 1998 Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci. 55, 3042–3064.2.0.CO;2>CrossRefGoogle Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639–656.CrossRefGoogle Scholar
Wilson, R., Dalaudier, F. & Bertin, F. 2005 Estimation of the turbulent fraction in the free atmosphere from MST radar measurements. J. Atmos. Ocean. Technol. 22, 1326–1339.CrossRefGoogle Scholar
Winters, K. B. & D'Asaro, E. A. 1996 Diascalar flux and the rate of fluid mixing. J. Fluid Mech. 317, 179–193.CrossRefGoogle Scholar
Winters, K. B., Lombard, P. N., Riley, J. J. & D'Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115–128.CrossRefGoogle Scholar
Xue, M., Droegemeier, K. K. & Wong, V. 2000 The Advanced Regional Prediction System (ARPS) – a multi-scale non hydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Met. Atmos. Phys. 75, 161–193.CrossRefGoogle Scholar
van, Zanten, M. C., Duynkerke, P. G. & Cuijpers, J. W. M. 1999 Entrainment parametrization in convective boundary layers. J. Atmos. Sci. 56, 813–828.Google Scholar
Zilitinkevich, S. S. 1991 Turbulent Penetrative Convection. Avebury Technical, Aldershot, UK.Google Scholar