• Ball, F. K., 1960: Control of inversion height by surface heating. Quart. J. Roy. Meteor. Soc., 86 , 483494.

  • Batchvarova, E., and S-E. Gryning, 1991: Applied model for the growth of the daytime mixed layer. Bound.-Layer Meteor., 56 , 261274.

  • Batchvarova, E., and S-E. Gryning, 1994: An applied model for the height of the daytime mixed layer and the entrainment zone. Bound.-Layer Meteor., 71 , 311323.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., 1973: Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Meteor. Soc., 99 , 178196.

  • Betts, A. K., 1974: Reply to comment on the paper “Non-precipitating cumulus convection and its parameterization.”. Quart. J. Roy. Meteor. Soc., 100 , 469471.

    • Search Google Scholar
    • Export Citation
  • Boers, R., 1989: A parameterization of the depth of the entrainment zone. J. Appl. Meteor., 28 , 107111.

  • Boers, R., and E. W. Eloranta, 1986: Lidar measurements of the atmospheric entrainment zone and the potential temperature jump across the top of the mixed layer. Bound.-Layer Meteor., 34 , 357375.

    • Search Google Scholar
    • Export Citation
  • Boers, R., E. W. Eloranta, and R. L. Coulter, 1984: Lidar observations of mixed layer dynamics: Tests of parameterized entrainment models of mixed layer growth rate. J. Climate Appl. Meteor., 23 , 247266.

    • Search Google Scholar
    • Export Citation
  • Carson, D. J., 1973: The development of a dry inversion-capped convectively unstable boundar layer. Quart. J. Roy. Meteor. Soc., 99 , 450467.

    • Search Google Scholar
    • Export Citation
  • Carson, D. J., and F. B. Smith, 1974: Thermodynamic model for the development of a convectively unstable boundary layer. Advances in Geophysics, H. E. Landsberg and J. Van Mieghem, Eds., Vol. 18A, Academic Press, 111–124.

    • Search Google Scholar
    • Export Citation
  • Caughey, S. J., 1982: Observed characteristics of the atmospheric boundary layer. Atmospheric Turbulence and Air Pollution Modelling, F. T. M. Nieuwstadt and H. van Dop, Eds., Reidel, 107–158.

    • Search Google Scholar
    • Export Citation
  • Caughey, S. J., and S. G. Palmer, 1979: Some aspects of turbulence structure through the depth of the convective boundary layer. Quart. J. Roy. Meteor. Soc., 105 , 811827.

    • Search Google Scholar
    • Export Citation
  • Chorley, L. G., S. J. Caughey, and C. J. Readings, 1975: The development of the atmospheric boundary layer: Three case studies. Meteor. Mag., 104 , 349360.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1970a: Preliminary results from numerical integration of the unstable boundary layer. J. Atmos. Sci., 27 , 12091211.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1970b: Convective velocity and temperature scales for the unstable planetary boundary layer and for Raleigh convection. J. Atmos. Sci., 27 , 12111213.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1974: Three dimensional numerical study of turbulence in an entraining mixed layer. Bound.-Layer Meteor., 7 , 199226.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1979: Prediction of convective mixed-layer entrainment for realistic capping inversion structure. J. Atmos. Sci., 36 , 424436.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18 , 495527.

  • Deardorff, J. W., and G. E. Willis, 1985: Further results from a laboratory model of the convective planetary boundary layer. Bound.-Layer Meteor., 32 , 205236.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., G. E. Willis, and D. K. Lilly, 1969: Laboratory investigation of non-steady penetrative convection. J. Fluid Mech., 35 , 731.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., G. E. Willis, and B. H. Stockton, 1980: Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech., 100 , 4164.

    • Search Google Scholar
    • Export Citation
  • Driedonks, A. G. M., 1982: Models and observations of the growth of the atmospheric boundary layer. Bound.-Layer Meteor., 23 , 283306.

    • Search Google Scholar
    • Export Citation
  • Driedonks, A. G. M., and H. Tennekes, 1984: Entrainment effects in the well-mixed atmospheric boundary layer. Bound.-Layer Meteor., 30 , 75103.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., 1995: Modeling the atmospheric convective boundary layer within a zero-order jump approach: An extended theoretical framework. J. Appl. Meteor., 34 , 19161928.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., 1998: Bulk models of the atmospheric convective boundary layer. Buoyant Convection in Geophysical Flows, E. J. Plate et al., Eds., Kluwer, 265–290.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., and D. V. Mironov, 1995: A model for shear-free convective boundary layer with parameterized capping inversion structure. J. Atmos. Sci., 52 , 8395.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., and R. Kaiser, 1998: Wind tunnel model study of turbulence regime in the atmospheric convective boundary layer. Buoyant Convection in Geophysical Flows, E. J. Plate et al., Eds., Kluwer, 327–370.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., and R. Conzemius, 2001: Large-eddy simulation of convective entrainment in linearly and discretely stratified fluids. Direct and Large-Eddy Simulation IV, B. J. Geurts et al., Eds., Kluwer, 435–442.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., and J. Thäter, 2001: Vertical transport of heat and momentum across a sheared density interface at the top of a horizontally evolving convective boundary layer. J. Turbul.,2, 007, 17 pp. [Available online at http://jot.iop.org/].

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., R. Kaiser, M. Rau, and E. Plate, 1996: Wind tunnel study of turbulent flow structure in the convective boundary layer capped by a temperature inversion. J. Atmos. Sci., 53 , 12731289.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., F. T. M. Nieuwstadt, and R. Kaiser, 2001a: Numerical and laboratory study of horizontally evolving convective boundary layer. Part I: Transition regimes and development of the mixed layer. J. Atmos. Sci., 58 , 7086.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., F. T. M. Nieuwstadt, and R. Kaiser, 2001b: Numerical and laboratory study of horizontally evolving convective boundary layer. Part II: Effects of elevated wind shear and surface roughness. J. Atmos. Sci., 58 , 546560.

    • Search Google Scholar
    • Export Citation
  • Fernando, H. J. S., 1991: Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech., 23 , 455493.

  • Filyushkin, B. N., and Yu Z. Miropolsky, 1981: Seasonal variability of the upper thermocline and self-similarity of temperature profiles. Okeanologia, 21 , 416424.

    • Search Google Scholar
    • Export Citation
  • Gryning, S-E., and E. Batchvarova, 1994: Parameterization of the depth of the entrainment zone above the daytime mixed layer. Quart. J. Roy. Meteor. Soc., 120 , 4758.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, S. J. Caughey, and C. J. Readings, 1976: Turbulence structure in a convective boundary layer. J. Atmos. Sci., 33 , 21522169.

    • Search Google Scholar
    • Export Citation
  • Kitaigorodskii, S. A., 1970: The Physics of Air–Sea Interaction (in Russian). Gidrometeoizdat, Leningrad, 284 pp. [English translation: Israel Program for Scientific Translation, 236 pp., 1973.].

    • Search Google Scholar
    • Export Citation
  • Kitaigorodskii, S. A., and Yu Z. Miropolsky, 1970: On the theory of open ocean active layer. Izv. Acad. Sci. USSR, Atmos. Oceanic Phys., 6 , 178188.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., 1998: Observations of clear and cloud-capped convective boundary layers, and techniques for probing them. Buoyant Convection in Geophysical Flows, E. J. Plate et al., Eds., Kluwer, 185–206.

    • Search Google Scholar
    • Export Citation
  • Lewellen, D. C., and W. S. Lewellen, 1998: Large-eddy boundary layer entrainment. J. Atmos. Sci., 55 , 26452665.

  • Lilly, D. K., 1968: Models of cloud-topped mixed layers under a strong inversion. Quart. J. Roy. Meteor. Soc., 94 , 292309.

  • Lilly, D. K., 2002: Entrainment into mixed layers. Part I: Sharp-edged and smoothed tops. J. Atmos. Sci., 59 , 33403352.

  • Lock, A. P., and M. K. MacVean, 1999: A parameterization of entrainment driven by surface heating and cloud-top cooling. Quart. J. Roy. Meteor. Soc., 125 , 271300.

    • Search Google Scholar
    • Export Citation
  • McGrath, J. L., H. J. S. Fernando, and J. C. R. Hunt, 1997: Turbulence, waves and mixing at shear-free density interfaces. Part 2. Laboratory experiments. J. Fluid Mech., 347 , 235261.

    • Search Google Scholar
    • Export Citation
  • Mironov, D. V., S. D. Golosov, S. S. Zilitinkevich, K. D. Kreiman, and A. Yu Terzhevik, 1991: Seasonal changes of temperature and mixing conditions in a lake. Modelling Air–Lake Interaction: Physical Background, S. S. Zilitinkevich, Ed., Springer-Verlag, 74–90.

    • Search Google Scholar
    • Export Citation
  • Nelson, E., R. Stull, and E. Eloranta, 1989: A prognostic relationship for entrainment zone thickness. J. Appl. Meteor., 28 , 885903.

  • Nieuwstadt, F. T. M., and R. A. Brost, 1986: Decay of convective turbulence. J. Atmos. Sci., 43 , 532546.

  • Otte, M. J., and J. C. Wyngaard, 2001: Stably stratified interfacial-layer turbulence from large-eddy simulation. J. Atmos. Sci., 58 , 34243442.

    • Search Google Scholar
    • Export Citation
  • Plate, E. J., 1971: Aerodynamic Characteristics of Atmospheric Boundary Layers. U.S. Atomic Energy Commission, 190 pp.

  • Schumann, U., and T. Gerz, 1995: Turbulent mixing in stably stratified shear flows. J. Appl. Meteor., 34 , 3348.

  • Sorbjan, Z., 1996: Effects caused by varying the strength of the capping inversion based on a large eddy simulation model of the shear-free convective boundary layer. J. Atmos. Sci., 53 , 20152024.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2001: An evaluation of local similarity at the top of the mixed layer based on large-eddy simulations. Bound.-Layer Meteor., 101 , 183207.

    • Search Google Scholar
    • Export Citation
  • Stevens, B., and D. H. Lenschow, 2001: Observations, experiments, and large eddy simulation. Bull. Amer. Meteor. Soc., 82 , 283294.

  • Stull, R. B., 1973: Inversion rise model based on penetrative convection. J. Atmos. Sci., 30 , 10921099.

  • Stull, R. B., 1976a: Mixed-layer depth model based on turbulent energetics. J. Atmos. Sci., 33 , 12681278.

  • Stull, R. B., 1976b: Internal gravity waves generated by penetrative convection. J. Atmos. Sci., 33 , 12791286.

  • Stull, R. B., and E. W. Eloranta, 1984: Boundary Layer Experiment 1983. Bull. Amer. Meteor. Soc., 65 , 450456.

  • Sullivan, P., C-H. Moeng, B. Stevens, D. H. Lenschow, and S. D. Mayor, 1998: Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci., 55 , 30423064.

    • Search Google Scholar
    • Export Citation
  • Tennekes, H., 1973: A model for the dynamics of the inversion above a convective boundary layer. J. Atmos. Sci., 30 , 558567.

  • Turner, J. S., 1968: The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech., 33 , 639656.

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 367 pp.

  • van Zanten, M. C., P. G. Duynkerke, and J. W. M. Cuijpers, 1999: Entrainment parameterization in convective boundary layers derived from large eddy simulations. J. Atmos. Sci., 56 , 813828.

    • Search Google Scholar
    • Export Citation
  • Willis, G. E., and J. W. Deardorff, 1974: A laboratory model of the unstable planetary boundary layer. J. Atmos. Sci., 31 , 12971307.

  • Wyngaard, J. C., and R. A. Brost, 1984: Top-down and bottom-up diffusion of a scalar in the convective boundary layer. J. Atmos. Sci., 41 , 102112.

    • Search Google Scholar
    • Export Citation
  • Zeman, O., and H. Tennekes, 1977: Parameterization of the turbulent energy budget at the top of the daytime atmospheric boundary layer. J. Atmos. Sci., 34 , 111123.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., 1975: Comments on “A model for the dynamics of the inversion above a convective boundary layer.”. J. Atmos. Sci., 32 , 991992.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., 1991: Turbulent Penetrative Convection. Avebury Technical, 179 pp.

  • Zilitinkevich, S. S., and J. W. Deardorff, 1974: Similarity theory for the planetary boundary layer of time-dependent height. J. Atmos. Sci., 31 , 14491452.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., and D. V. Mironov, 1992: Theoretical model of the thermocline in a freshwater basin. J. Phys. Oceanogr., 22 , 988996.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., E. E. Fedorovich, and M. V. Shabalova, 1992: Numerical model of a non-steady atmospheric planetary boundary layer, based on similarity theory. Bound.-Layer Meteor., 59 , 387411.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 288 75 9
PDF Downloads 137 58 8

Convective Entrainment into a Shear-Free, Linearly Stratified Atmosphere: Bulk Models Reevaluated through Large Eddy Simulations

View More View Less
  • 1 School of Meteorology, University of Oklahoma, Norman, Oklahoma
  • | 2 German Weather Service, Offenbach am Main, Germany
Restricted access

Abstract

Relationships between parameters of convective entrainment into a shear-free, linearly stratified atmosphere predicted by the zero-order jump and general-structure bulk models of entrainment are reexamined using data from large eddy simulations (LESs). Relevant data from other numerical simulations, water tank experiments, and atmospheric measurements are also incorporated in the analysis. Simulations have been performed for 10 values of the buoyancy gradient in the free atmosphere covering a typical atmospheric stability range. The entrainment parameters derived from LES and relationships between them are found to be sensitive to the model framework employed for their interpretation. Methods of determining bulk model entrainment parameters from the LES output are proposed and discussed.

Within the range of investigated free-atmosphere stratifications, the LES predictions of the inversion height and buoyancy increment across the inversion are found to be close to the analytical solutions for the equilibrium entrainment regime, which is realized when the rate of time change of the CBL-mean turbulence kinetic energy and the energy drain from the CBL top are both negligibly small. The zero-order model entrainment ratio of about 0.2 for this regime is generally supported by the LES data. However, the zero-order parameterization of the entrainment layer thickness is found insufficient. A set of relationships between the general-structure entrainment parameters for typical atmospheric stability conditions is retrieved from the LES. Dimensionless constants in these relationships are estimated from the LES and laboratory data. Power-law approximations for relationships between the entrainment parameters in the zero-order jump and general-structure bulk models are evaluated based on the conducted LES. In the regime of equilibrium entrainment, the stratification parameter of the entrainment layer, which is the ratio of the buoyancy gradient in the free atmosphere to the overall buoyancy gradient across the entrainment layer, appears to be a constant of about 1.2.

Corresponding author address: Dr. Evgeni Fedorovich, Sarkeys Energy Center, 100 East Boyd, School of Meteorology, University of Oklahoma, Norman, OK 73019-1013. Email: fedorovich@ou.edu

Abstract

Relationships between parameters of convective entrainment into a shear-free, linearly stratified atmosphere predicted by the zero-order jump and general-structure bulk models of entrainment are reexamined using data from large eddy simulations (LESs). Relevant data from other numerical simulations, water tank experiments, and atmospheric measurements are also incorporated in the analysis. Simulations have been performed for 10 values of the buoyancy gradient in the free atmosphere covering a typical atmospheric stability range. The entrainment parameters derived from LES and relationships between them are found to be sensitive to the model framework employed for their interpretation. Methods of determining bulk model entrainment parameters from the LES output are proposed and discussed.

Within the range of investigated free-atmosphere stratifications, the LES predictions of the inversion height and buoyancy increment across the inversion are found to be close to the analytical solutions for the equilibrium entrainment regime, which is realized when the rate of time change of the CBL-mean turbulence kinetic energy and the energy drain from the CBL top are both negligibly small. The zero-order model entrainment ratio of about 0.2 for this regime is generally supported by the LES data. However, the zero-order parameterization of the entrainment layer thickness is found insufficient. A set of relationships between the general-structure entrainment parameters for typical atmospheric stability conditions is retrieved from the LES. Dimensionless constants in these relationships are estimated from the LES and laboratory data. Power-law approximations for relationships between the entrainment parameters in the zero-order jump and general-structure bulk models are evaluated based on the conducted LES. In the regime of equilibrium entrainment, the stratification parameter of the entrainment layer, which is the ratio of the buoyancy gradient in the free atmosphere to the overall buoyancy gradient across the entrainment layer, appears to be a constant of about 1.2.

Corresponding author address: Dr. Evgeni Fedorovich, Sarkeys Energy Center, 100 East Boyd, School of Meteorology, University of Oklahoma, Norman, OK 73019-1013. Email: fedorovich@ou.edu

Save