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Laboratory studies of the entrainment zone of a convectively mixed layer

Published online by Cambridge University Press:  19 April 2006

J. W. Deardorff ,
G. E. Willis  and
B. H. Stockton
J. W. Deardorff
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
G. E. Willis
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
B. H. Stockton
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
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Abstract

In laboratory experiments of simulated atmospheric mixed layers the entrainment zone is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam. The region of negative buoyancy flux of entrainment is found to be confined between the outermost height reached by the few most vigorous penetrating parcels, and by the lesser height where mixed-layer fluid occupies, usually, some 90 to 95% of the total area. The height of most negative buoyancy flux of entrainment is found to agree roughly with the level at which mixed-layer fluid occupies half the area.

The thickness of the entrainment zone, relative to the depth of the well-mixed layer just beneath, is found to be quite substantial (0·2 to 0·4), and apparently decreases only asymptotically with increasing ‘overall’ Richardson number, Ri*. The thickness is not well predicted by parcel theory.

Extensive detrainment is found to occur within the entrainment zone, and adds to the difficulty in defining the position of the local interface between mixed-layer fluid and unmodified fluid.

For typical Ri* values occurring in the atmosphere, the dimensionless entrainment rate is found to be given satisfactorily by 0·25(Ri*)−1, although an $(Ri^{*})^{\frac{3}{2}}$ dependence cannot be ruled out by the present data. Entrainment into a neutral layer in the absence of a capping inversion is found to proceed at the expected rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 1 , 11 September 1980 , pp. 41 - 64
Copyright
© 1980 Cambridge University Press

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References

Betts, A. K. 1973 Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Met. Soc. 99, 178–196.Google Scholar
Betts, A. K. 1976 Modeling subcloud layer structure and interaction with a shallow cumulus layer. J. Atmos. Sci. 33, 2363–2382.Google Scholar
Carson, D. J. & Smith, F. B. 1974 Thermodynamic model for the development of a convectively unstable boundary layer. In Advances in Geophysics, vol. 18A (ed. H. E. Landsberg & J. Van Mieghem), pp. 111–124. Academic.
Deardorff, J. W. 1969 Numerical study of heat transport by internal gravity waves above a growing unstable layer. Phys. Fluids Suppl. II 184–194.Google Scholar
Deardorff, J. W. 1974 Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Boundary-Layer Met. 7, 81–106.Google Scholar
Deardorff, J. W. 1976 On the entrainment of a stratocumulus-topped mixed layer. Quart. J. Roy. Met. Soc. 102, 563–582.Google Scholar
Deardorff, J. W. 1979 Prediction of convective mixed-layer entrainment for realistic capping inversion structure. J. Atmos. Sci. 36, 424–436.Google Scholar
Deardorff, J. W., Willis, G. E. & Lilly, D. K. 1969 Laboratory investigation of non-steady penetrative convection. J. Fluid Mech. 35, 7–31.Google Scholar
Dickinson, S. C. & Long, R. R. 1978 Laboratory study of the growth of a turbulent layer of fluid. Phys. Fluids 21, 1698–1701.Google Scholar
Gaynor, J. E. & Mandics, P. A. 1978 Analysis of the tropical marine boundary layer during GATE using acoustic sounder data. Mon. Weath. Rev. 106, 223–232.Google Scholar
Goodman, J. K. & Miller, A. 1976 Mass transport across a temperature inversion. San Jose State Univ., Dept. of Met., Rep. no. 76–10.Google Scholar
Hall, F. F., Edinger, J. G. & Neff, W. D. 1975 Convective plumes in the planetary boundary layer, investigated with an acoustic sounder. J. Appl. Met. 14, 513–523.Google Scholar
Hardy, K. R. & Ottersten, H. 1969 Radar investigations of convective patterns in the clear atmosphere. J. Atmos. Sci. 26, 666–672.Google Scholar
Kahn, P. H. & Businger, J. A. 1978 The effect of radiative flux divergence on entrainment of a saturated convective boundary layer. Quart. J. Roy. Met. Soc. 105, 303–305.Google Scholar
Kantha, L. H. 1979a On generation of internal waves by turbulence in the mixed layer. Dyn. Atmos. & Oceans 3, 39–46.Google Scholar
Kantha, L. H. 1979b Comparison of Kantha entrainment model with other slab models. Ocean Modelling 26, 6–9. D.A.M.T.P., University of Cambridge.Google Scholar
Kantha, L. H. 1979c Turbulent entrainment at a bouyancy interface due to convective turbulence. Unpublished manuscript, Dept. of Earth and Plan. Sci., Johns Hopkins Univ., Baltimore, Maryland 21218.
Kantha, L. H., Phillips, O. M. & Azad, R. S. 1977 On turbulent entrainment at a stable density interface. J. Fluid Mech. 79, 753–768.Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–655.Google Scholar
Kunkel, K. E., Eloranta, E. W. & Shipley, S. T. 1977 Lidar observations of the convective boundary layer. J. Appl. Met. 16, 1306–1311.Google Scholar
Lilly, D. K. & Schubert, W. H. 1979 The effects of radiative cooling in a cloud-topped mixed layer. J. Atmos. Sci. 37, 482–487.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71, 385–405.Google Scholar
Linden, P. F. & Crapper, P. F. 1974 Effect of molecular diffusion on the structure of a turbulent density interface. In Advances in Geophysics, vol. 18A (ed. H. E. Landsberg & J. Van Mieghem), pp. 433–443. Academic.
Long, R. R. & Kantha, L. H. 1978 The rise of a strong inversion caused by heating at the ground. In Proc. 12th Naval Hydrodyn. Symp., Wash. D.C. National Academy of Sciences.
Malkus, J. S. 1958 On the structure of the trade wind moist layer. Papers in Phys. Oceanog. & Met. 13, M.I.T. and Woods Hole Oceanog. Inst. 1–48.Google Scholar
Moore, M. J. & Long, R. R. 1971 An experimental investigation of turbulent stratified shearing flow. J. Fluid Mech. 49, 635–655.Google Scholar
Namias, J. 1939 On the dissipation of tall cumulus clouds. Monthly Weather Rev. 67, 294–295.Google Scholar
Phillips, O. M. 1972 The entrainment interface. J. Fluid Mech. 51, 97–118.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. 2nd edn. Cambridge University Press.
Price, J. F. 1979 Observations of a rain-formed mixed layer. J. Phys. Oceanog. 9, 643–649.Google Scholar
Price, J. F., Mooers, C. N. K. & Van Leer, J. C. 1978 Observation and simulation of storm-induced mixed-layer deepening. J. Phys. Oceanog. 8, 582–599.Google Scholar
Randall, D. A. 1980 Entrainment into a stratocumulus layer with distributed radiative cooling. J. Atmos. Sci. 37, 148–159.Google Scholar
Rayment, R. & Readings, C. J. 1974 A case study of the structure and energetics of an inversion. Quart. J. Roy. Met. Soc. 100, 221–233.Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 23, 639–656.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Uthe, E. E. 1972 Lidar observations of the urban aerosol structure. Bull. Am. Met. Soc. 53, 358–360.Google Scholar
Willis, G. E. & Deardorff, J. W. 1974 A laboratory model of the unstable planetary boundary layer. J. Atmos. Sci. 31, 1297–1307.Google Scholar
Wyatt, L. R. 1978 The entrainment interface in a stratified fluid. J. Fluid Mech. 86, 293–311.Google Scholar
Zeman, O. & Tennekes, H. 1977 Parameterization of the turbulent energy budget at the top of the daytime atmospheric boundary layer. J. Atmos. Sci. 34, 111–123.Google Scholar