Roll vortices in the planetary boundary layer: A review

Dieter Etling1, Robert A. Brown2
1Institut für Meteorologie und Klimatologie, Universität Hannover, Hannover 21, Germany
2Department of Atmospheric Sciences, University of Washington, Seattle, USA

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Agee, E.M.: 1982, ?An Introduction to Shallow Convective Systems?. In: Cloud Dynamics (E.M. Agee and T. Asai, Eds), D. Reidel, Dordrecht, 3?30.

Asai, T.: 1970, ?Stability of Plane Parallel Flow with Variable Vertical Shear and Unstable Stratification?,J. Meteorol. Soc. Japan 48, 129?139.

Asai, T., and Nakasuji, I.: 1973, ?The Stability of Ekman Boundary Flow with Thermally Unstable Stratification?,J. Meterol. Soc., Japan 51, 29?42.

Atlas, D., Walter, B., Chou, S.-H. and Sheu, P.J.: 1986, ?The Structure of the Unstable Marine Boundary Layer Viewed by Lidar and Aircraft Observations?,J. Atmos. Sci. 43, 1301?1318.

Becker, P.: 1987, ?Three Dimensional Investigations of Roll Vortices: A Case Study?,Beitr. Phys. Atmosph. 60, 170?179.

Bennetts, D.A., and Hoskins, B.J.: 1979, ?Conditional Symmetric Instability ? Possible Explanation for Frontal Rainbands?,Quart. J. Roy. Meteorol. Soc. 105, 945?962.

Brown, R.A.: 1970, ?A Secondary Flow Model for the Planetary Boundary Layer?,J. Atmos. Sci. 27, 742?757.

Brown, R.A.: 1972, ?On the Inflection Point Instability of a Stratified Ekman Boundary Layer?,J. Atmos. Sci. 29, 850?859.

Brown, R.A.: 1974a, ?Analytic Methods in Planetary Boundary Layer Modeling?, Adam Hilger LTD., London, and Halstead Press, John Wiley and Sons, New York, 150 pp.

Brown, R.A.: 1974b, ?Matching Classical Boundary Layer Solutions Toward a Geostrophic Drag Coefficient Relation?,Boundary-Layer Meteorol. 7, 489?500.

Brown, R.A.: 1980, ?Longitudinal Instabilities and Secondary Flows in the Planetary Boundary Layer: A Review?,Rev. Geophys. Space Phys. 18, 683?697.

Brown, R.A.: 1981, ?On the Use of Exchange Coefficients in Modelling Turbulent Flow?,Boundary-Layer Meteorol. 20, 111?116.

Brown, R.A.: 1991, ?Fluid Mechanics of the Atmosphere?,Academic Press, Vol. 47 of the International Geophysics Series, 497 pp.

Brown, R.A. and R. Foster: 1991, ?Comparison of a 1-D Analytic PBL Model with Secondary Flow and a Second-Order Closure Model Using GCM Data?,Proceedings of AGU Fall Meeting, San Francisco, EOS 72, Supplement, 79.

Brown, R.A. and T. Liu: 1982, ?An Operational Large-Scale Marine Planetary Boundary Layer Model?,J. Applied Meteorol. 21, 261?269.

Brown, R.A. and G. Levy: 1986, ?Ocean Surface Pressure Fields from Satellite Sensed Winds?,Mon. Wea. Rev. 114, 2197?2206.

Brümmer, B.: 1985, ?Structure, Dynamics and Energetics of Boundary Layer Rolls from KonTur Aircraft Observations?,Beitr. Phys. Atmosph. 58, 237?254.

Brümmer, B., Latif, M.: 1985, ?Some Studies on Inflection Point Instability?,Beitr. Phys. Atmosph. 58, 117?126.

Brümmer, B., Bakan, S. and Hinzpeter, H.: 1985, ?KONTUR: Observations of Cloud Streets and Open Cellular Structures?,Dyn. Atmos. Oceans 9, 281?296.

Busse, F.H.: 1978, ?Non-linear Properties of Thermal Convection?,Rep. Prog. Phys. 41, 1929?1967.

Caldwell, D.R., and Van Atta, C.W.: 1970, ?Characteristics of Ekman Boundary Layer Instabilities?,J. Fluid Mech. 44, 79?95.

Chlond, A.: 1985, ?A Study of Roll Vortices in the Atmospheric Boundary Layer?,Beitr. Phys. Atmos. 58, 17?30.

Chlond, A.: 1987, ?A Numerical Study of Horizontal Roll Vortices in Neutral and Unstable Atmospheric Boundary Layers?,Beitr. Phys. Atmosph. 60, 144?169.

Chlond, A.: 1988, ?Numerical and Analytical Studies of Diabatic Heating Effect upon Flatness of Boundary Layer Rolls?,Beitr. Phys. Atmosph. 61, 312?329.

Chlond, A.: 1992, ?Three-Dimensional Simulation of Cloud Street Development During a Cold Air Outbreak?,Boundary-Layer Meteorol. 58, 161?200.

Chou, S.-H., Atlas, D. and Yeh, E.-N.: 1986, ?Turbulence in a Convective Marine Atmospheric Boundary Layer?,J. Atmos. Sci. 43, 547?564.

Chou, S.-H. and Zimmermann, J.: 1989, ?Bivariate Conditional Sampling of Buoyancy Flux during an Intense Cold-Air Outbreak?,Boundary-Layer Meteorol. 46, 93?112.

Chou, S.H. and Ferguson, M.D.: 1991, ?Heat Fluxes and Roll Circulations over the Western Gulf Stream during an Intense Cold-Air Outbreak?,Boundary-Layer Meteorol. 55, 255?282.

Christian, T.W. and Wakimoto, R.M.: 1989, ?The Relationship Between Radar Reflectivities and Clouds Associated with Horizontal Roll Convection on 8 August 1982?,Mon. Wea. Rev. 117, 1530?1544.

Chrobok, G., Raasch, S. and Etling, D.: 1992, ?A Comparison of Local and Non-Local Turbulence Closure Methods for the Case of a Cold Air Outbreak?,Boundary-Layer Meteorol. 58, 69?90.

Clark, T.L., Hauf, T. Kuettner, J.P.: 1986, ?Convectively Forced Internal Gravity Waves: Results from Two-Dimensional Numerical Experiments?,Quart. J. Roy. Meteorol. Soc. 112, 899?925.

Coleman, G.N., Ferzinger, J.H. and Spalart, P.R.: 1990, ?A Numerical Study of the Turbulent Ekman Layer?,J. Fluid Mech. 213, 313?348.

Coleman, G.N.: 1990, ?A Numerical Study of the Stratified Turbulent Ekman Layer?,Ph D. thesis, Dep. Mechanical Engineering, Stanford University.

Criminale, W.O. and Spooner, G.F.: 1981, ?Maintenance of Oscillations in a Turbulent Ekman Layer?,Boundary-Layer Meteorol. 21, 407?421.

Deardorff, J.W.: 1972, ?Numerical Investigation of Neutral and Unstable Planetary Boundary Layers?,J. Atmos. Sci. 29, 91?115.

Drazin, P.G. and Reid, W.H.: 1981, ?Hydrodynamic Stability?,Cambridge University Press, 525 pp

Emanuel, K.A.: 1979, ?Inertial Instabaility and Mesoscale Convective Systems. Part I: Linear Theory of Inertial Instability in Rotating Viscous Fluids?,J. Atmos. Sci. 36, 2425?2449.

Etling, D.: 1971, ?The Stability of an Ekman Boundary Flow as Influenced by Thermal Stratification?,Beitr. Phys. Atmosph. 44, 168?186.

Etling, D. and Wippermann, F.: 1975, ?On the Instability of a Planetary Boundary Layer with Rossby-Number Similarity?,Boundary-Layer Meteorol. 9, 341?360.

Etling, D. and Raasch, S.: 1987, ?Numerical Simulation of Vortex Roll Development During a Cold Air Outbreak?,Dyn. Atmos. Oceans 10, 277?290.

Eymard, L.: 1985, ?Convective Organization in a Tropical Boundary Layer: An Interpretation of Doppler Radar Observations Using Asai's Model?,J. Atmos. Sci. 42, 2844?2855.

Eymard, L. and Weill, A.: 1988, ?Dual Doppler Radar Investigation of the Tropical Convective Boundary Layer?,J. Atmos. Sci. 45, 853?864.

Faller, A.J. and Auer, S.J.: 1987, ?The Roles of Langmuir Circulation in the Dispersion of Surface Tracers?,J. Phys. Oceanogr. 18, 1108?1123.

Faller, A.J. and Kaylor, R.E.: 1966, ?A Numerical Study of the Laminar Ekman Layer?,J. Atmos. Sci. 23, 466?480.

Faller, A.J. and Kaylor, R.E.: 1967, ?Instability of the Ekman Spiral with Applications to the Planetary Boundary Layer?,Phys. Fluids 10, 212?219.

Foster, R. and R.A. Brown: 1991, ?An Investigation into the Importance of Stratification, Thermal Wind, Non-Stationarity and Rolls in PBL Parameterizations?,Proceedings of AGU Fall Meeting, San Francisco, EOS 72, Supplement, 79.

Gammelsrod, T.: 1975, ?Instability of Couette Flow in a Rotating System and Origin of Langmuir Circulations?,J. Geophys. Res. 80, 5069?5075.

Gerling, T.W.: 1986, ?Structure of the Surface Wind Field from the Seasat SAR?,J. Geophys. Res. 91, 2308?2320.

Gossard, Earl E. and Moninger, W.R.: 1975, ?The Influence of a Capping Inversion on the Dynamic and Convective Instability of a Boundary Layer Model with Shear?,J. Atmos. Sci. 32, 2111?2124.

Grossman, R.L.: 1982, ?An Analysis of Vertical Velocity Spectra Obtained in theBOMEX Fair-Weather, Trade-Wind Boundary Layer?,Boundary-Layer Meteorol. 23, 323?357.

Grossman, R.L. and Betts, A.K.: 1990, ?Air-Sea Interaction During an Extreme Cold Air Outbreak from the Eastern Coast of the United States?,Mon. Wea. Rev. 118, 324?342.

Haack, T., and Shirer, H.N.: 1992, ?Mixed Convective-Dynamic Roll Vortices and their Effects on Initial Wind and Temperature Profiles?,J. Atmos. Sci. 49, 1181?1201.

Haines, D.A.: 1982, ?Horizontal Roll Vortices and Crown Fires?,J. Appl. Meteorol. 21, 751?762.

Hauf, T. and Clark, T.L.: 1989, ?Three-Dimensional Numerical Experiments on Convectively Forced Internal Gravity Waves?,Quart. J. Roy. Meteorol. Soc. 115, 309?333.

Hein, P. and Brown, R.A.: 1988, ?Observations of Longitudinal Roll Vortices During Arctic Cold Air Outbreaks over Open Water?,Boundary Layer Meteorol. 45, 177?199.

Helfand, H.M. and Kalnay, E.: 1983, ?A Model to Determine Open or Closed Cellular Convection?,J. Atmos. Sci. 40, 631?650.

Huerre, C.H.: 1984, ?Perturbed Free Shear Layers?,Ann. Rev. Fluid Mech. 16, 305?424.

Kaylor, R.E. and Faller, A.J.: 1972, ?Instability of the Stratified Ekman Boundary Layer and the Generation of Internal Waves?,J. Atmos. Sci. 29, 497?509.

Kelly, R.E., 1977, ?The Onset and Development of Rayleigh-Benard Convection in Shear Flows: A Review?,Physicochemical Hydrodynamics (B.B. Spalding, Ed.), Advance Publications 65-79.

Kelly, R.D.: 1982, ?A Single Doppler Radar Study of Horizontal Roll Convection in a Lake-Effect Snowstorm?,J. Atmos. Sci. 39, 1521?1531.

Kelly, R.D.: 1984, ?Horizontal Roll and Boundary Layer Interrelationships Observed over Lake Michigan?,J. Atmos. Sci. 41, 1816?1826.

Krishnamurti, R.: 1975, ?On Cellular Cloud Patterns. Parts 1-3?,J. Atmos. Sci. 32, 1355?1383.

Kropfli, R.A., and Kohn, N.M.: 1978, ?Persistent Horizontal Rolls in the Urban Mixed Layer as Revealed by Dual-Doppler-Radar?,J. Appl. Meteorol. 17, 669?676.

Küttner, J.P.: 1959, ?The Band structure of the Atmosphere?,Tellus 11, 267?294.

Küttner, J.P.: 1971, ?Cloud Bands in the Atmosphere?,Tellus 23, 404?425.

Leibovich, S.: 1983, ?The Flow and Dynamics of Langmuir Circulations?,Ann. Rev. Fluid. Mech. 15, 391?427.

Leibovich, S., and Lele, S.K.: 1985, ?The Influence of the Horizontal Component of Earth's Angular Velocity on the Stability of the Ekman Layer?,J. Fluid. Mech. 150, 41?87.

LeMone, M.A.: 1973, ?The Structure and Dynamics of Horizontal Roll Vortices in the Planetary Boundary Layer?,J. Atmos. Sci. 30, 1077?1091.

LeMone, M.A.: 1976, ?Modulation of Turbulence Energy by Longitudinal Rolls in an Unstable Boundary Layer?,J. Atmos. Sci. 33, 1308?1320.

LeMone, M.A. and Pennell, W.T.: 1976, ?The Relationship of Trade Wind Cumulus Distribution to Subcloud Layer Fluxes and Structure?,Mon. Wea. Rev. 101, 524?539.

LeMone, M.A. and Meitin, R.J.: 1984, ?Three Examples of Fair-Weather Mesoscale Boundary Layer Convection in the Tropics?,Mon. Wea. Rev. 112, 1985?1997.

Lilly, D.K.: 1966, ?On the Instability of Ekman Boundary Flow?J. Atmos. Sci. 23, 481?494.

Lilly, D.K. and Schneider, J.M.: 1990, ?Dual Doppler Measurements of Momentum Flux: Results From the PHOENIX II Study of the Convective Boundary Layer?,Proc. 9th. Symp. Turb. Diff., Roskilde, Denmark, Amer. Meteorol. Soc., Boston, 98?101.

Liu, J.I.C.: 1989, ?Coherent Structures in Transitional and Turbulent Free Shear Flows?,Ann. Rev. Fluid Mech. 21, 285?315.

Martin, T. and Bakan, S.: 1991, ?Airplane Investigation of a Case of Convective Cloud Bands over the North Sea?,Boundary Layer-Meteorol. 50, 359?380.

Mason, P.J.: 1983, ?On the Influence of Variation in Monin-Obukhov Length on Horizontal Roll Vortices in an Inversion-Capped Planetary Boundary Layer?,Boundary-Layer Meteorol. 27, 43?68.

Mason, P.J.: 1985, ?A Numerical Study of Cloud Streets in the Planetary Boundary Layer?,Boundary-Layer Meteorol. 32, 281?304.

Mason, P.J.: 1989, ?Large-Eddy Simulation of the Convective Atmospheric Boundary Layer?,J. Atmos. Sci. 46, 1492?1516.

Mason, P.J. and Sykes, R.I.: 1980, ?A Two-Dimensional Numerical Study of Horizontal Roll Vortices in the Neutral Atmospheric Boundary Layer?,Q. J. R. Meteorol. Soc. 106, 351?366.

Mason, P.J. and Sykes, R.I.: 1982, ?A Two-Dimensional Numerical Study of Horizontal Roll Vortices in an Inversion Capped Planetary Boundary Layer?,Q. J. R. Meteorol. Soc. 108, 801?823.

Mason, P.J. and Thomson, D.J.: 1987, ?Large-Eddy Simulations of the Neutral-Static-Stability Planetary Boundary Layer?,Q. J. R. Meteorol. Soc. 113, 413?443.

Melfi, S.H., Spinhirne, J.D., Chou, S.-H. and Palm, S.P.: 1985, ?Lidar Observations of Vertically Organized Convection in the Planetary Boundary Layer over the Ocean?,J. Climate Appl. Meteorol. 24, 806?821.

Mikhaylova, L.A. and Ordanovich, A.Y.: 1991, ?Coherent Structures in the Atmospheric Boundary Layer?,Izv. Atm. Ocean. Phys. 27, 413?427.

Miura, Y.: 1986, ?Aspect Ratios of Longitudinal Rolls and Convection Cells Observed During Cold Air Outbreaks?,J. Atmos. Sci. 43, 26?39.

Moeng, C.H.: 1984, ?A Large Eddy Simulation for the Study of Planetary Boundary Layer Turbulence?J. Atmos. Sci. 41, 2052?2062.

Moeng, C.H. and Wyngaard, J.C.: 1989, ?Evaluation of Turbulent Transport and Dissipation Closures in Second-Order Modeling?,J. Atmos. Sci. 46, 2311?2330.

Mourad, P.D., Brown, R.A.: 1990, ?On Multiscale Large Eddy States in Weakly Stratified Planetary Boundary Layers?,J. Atmos. Sci. 47, 414?438.

Müller, D., Etling, D., Kottmeier, Ch. and Roth, R.: 1985, ?On the Occurrence of Cloud Streets over Northern Germany?,Q. J. R. Meteorol. Soc. 111, 761?772.

Nieuwstadt, F.T.M. and Brost, R.A.: 1986, ?The Decay of Convective Turbulence?,J. Atmos. Sci. 43, 532?546.

Pennell, W.T. and LeMone, M.A.: 1974, ?An Experimental Study of Turbulence Structure in the Fair-Weather Trade Wind Boundary Layer?,J. Atmos. Sci. 31, 1308?1323.

Priestley, C.H.B.: 1962, ?Width-Height Ratio of Large Convection Cells?,Tellus 14, 123?124.

Puhakka, T., and Saarikivi, P.: 1986, ?Doppler Radar Observations on Horizontal Roll Vortices in Finnland?,Geophysica 22, 101?118.

Raasch, S.: 1988, ?Numerische Simulation zur Entwicklung von Wirbelrollen und konvektiver Grenzschicht bei Kaltluftausbrüchen über dem Meer?,Ph D. Thesis, Dept. of Physics University of Hannover, 154 pp.

Raasch, S.: 1990 a, ?Numerical Simulation of the Development of the Convective Boundary Layer During a Cold Air Outbreak?,Boundary Layer Meteorol. 52, 349?375.

Raasch, S.: 1990 b, ?Two Numerical Studies of Horizontal Roll Vortices in Near-Neutral Inversion Capped Planetary Boundary Layers?,Beitr. Phys. Atmosph. 63, 205?227.

Raasch, S. and Etling, D.: 1991, ?Numerical Simulation of Rotating Turbulent Thermal Convection?,Beitr. Phys. Atmosph. 64, 185?199.

Rabin, R.M., Doviak, R.J. and Sundara-Rajan, A.: 1982, ?Doppler Radar Observations of Momentum Flux in a Cloudless Convective Layer with Rolls?,J. Atmos. Sci. 39, 851?863.

Ray, D.: 1986, ?Variable Eddy Diffusivities and Atmospheric Cellular Convection?,Boundary-Layer Meteorol. 30, 117?131.

Reinking, R.F., Doviak, R.J. and Gilmer, R.O.: 1981, ?Clear-Air Roll Vortices and Turbulent Motions as Detected with an Airborne Gust Probe and Dual-Doppler Radar?,J. Appl. Meteorol. 20, 678?685.

Robinson, S.K.: 1991, ?Coherent Motions in the Turbulent Boundary Layer?,Ann. Rev. Fluid Mech. 23, 601?640.

Rothermal, J. and Agee, E.M.: 1986, ?A Numerical Study of Atmospheric Convective Scaling?,J. Atmos. Sci. 43, 1185.

Schumann, U. and Friedrich, R.: 1986, ?Direct and Large Eddy Simulation of Turbulence?, Vieweg, Braunschweig, 340 pp

Sang, J.G.: 1991, ?On Formation of Convective Roll Vortices Internal Gravity Waves: A Theoretical Study?,Meteorol. Atmos. Phys. 46, 15?28.

Schmidt, H. and Schumann, U.: 1989, ?Coherent Structure of the Convective Boundary Layer Derived from Large-Eddy Simulations?,J. Fluid Mech. 200, 511?562.

Schols, J.L.J.: 1984, ?The Detection and Measurement of Turbulent Structures in the Atmospheric Surface Layer?,Boundary-Layer Meteorol. 29, 39?58.

Schols, J.L.J., Jansen, A.E. and Krom, J.G.: 1985, ?Characteristics of Turbulent Structures in the Unstable ASL?,Boundary-Layer Meteorol. 33, 173?196.

Scorer, R.S.: 1986, ?Cloud Investigation by Satellite?, Ellis Horwood, Chichester, 300 pp.

Scorer, R.S.: 1990, ?Satellite as Microscope?, Ellis Horwood, Chichester, 286 pp.

Sheu, P.J., Agee, E.M. and Tribia, J.J.: 1980, ?A Numerical Study of Physical, Processes Affecting Convective Cellular Geometry?,J. Meteorol. Soc. Japan 58, 489?498.

Shirer, H.N.: 1986, ?On Cloud Street Development in Three Dimensions: Parallel and Rayleigh Instabilities?,Beitr. Phys. Atmosph. 59, 126?149.

Shirer, H.N. and Brümmer, B.: 1986, ?Cloud Streets During KonTur. A Comparison of Parallel/Thermal Instability Modes With Observations?,Beitr. Phys. Atmosph. 59, 150?161.

Smedman, A.S.: 1991, ?Occurrence of Roll Circulations in a Shallow Boundary Layer?,Boundary-Layer Meteorol. 57, 343?358.

Stensrud, D.J., and Shirer, H.N.: 1988, ?Development of Boundary Layer Rolls from Dynamic Instabilities?,J. Atmos. Sci. 45, 1007?1019.

Streten, N.A.: 1975, ?Cloud Cell Size and Pattern Evolution in Arctic Air Advection over the North Pacific?,Arch. Met. Geophys. Biokl. A24, 213?228.

Stull, R.B.: 1991, ?A Comparison of Parameterized vs. Measured Transilient Mixing Coefficients for a Convective Mixed Layer?,Boundary-Layer-Meteorol.,55, 67?90.

Sykes, R.I., Lewellen, W.S. and Henn, D.S.: 1988, ?A Numerical Study of the Development of Cloud-Street Spacing?,J. Atmos. Sci. 45, 2556?2569.

Sykes, R.I., Lewellen, W.S. and Henn, D.S.: 1990, ?Numerical Simulation of the Boundary Layer Structure during Cold Air Outbreak of GALE IOP-2?,Mon. Wea. Rev. 118, 363?374.

Thomson, T.W., Liu, W.T. and Weissman, D.E.: 1983, ?Synthetic Aperture Radar Observation of Ocean Roughness from Rolls in an Unstable Marine Boundary Layer?,Geophys. Res. Let. 12, 1172?1175.

Thorpe, S.A.: 1992, ?The Breakup of Langmuir Circulation and the Instability of an Array of Vortices?,J. Phys. Oceanogr. 22, 350?360.

Troen and Mahrt, L.: 1986, ?A Simple Boundary-Layer Model and its Sensitivity to Surface Evaporation?,Boundary-Layer-Meteorol. 37, 107?128.

van Delden, A.: 1985, ?Convection in Polar Outbreaks and related Phenomena?,Proc. Workshop. Institute of Meteorology and Oceanography, University of Utrecht, Netherlands, 163 pp.

van Delden, A. and Oerlemans, J.: 1982, ?Grouping of Clouds in a Numerical Cumulus Convection Model?,Beitr. Phys. Atmosph. 55, 239?252.

Walter, B.A.: 1980, ?Wintertime Observations of Roll Clouds over the Bering Sea?,Mon. Wea. Rev. 108, 2024?2031.

Walter, B.A.: 1986, ?The Mesoscale Organization, Dynamics and Evolution of the Marine Planetary Boundary Layer during Cold Air Outbreaks?,Ph. D. Thesis Dept. Atmosph. Sciences, University of Washington, Seattle pp 200.

Walter, B.A. and Overland, J.E.: 1984, ?Observations of Longitudinal Rolls in a Near Neutral Atmosphere?,Mon. Wea. Rev. 112, 200?208.

Weston, K.J.: 1980, ?An Observational Study of Convective Cloud Streets?,Tellus 32, 433?438.

Weil, J.C.: 1990, ?A Diagnostis of the Asymmetry in Top-Down and Bottom-Up Diffusion using a Lagrangian Stochastic Model?,J. Atmos. Sci. 47, 501?515.

Wilczak, J.M. and Businger, J.A.: 1984, ?Large Scale Eddies in the Unstably Stratified Atmospheric Surface Layer. Part 1 (Wilczak): Velocity and Temperature Structure. Part 2 (Wilczak and Businger): Turbulent Pressure Fluctuations and the Budgets of Heat Flux, Stress and T.K.E.?,J. Atmos. Sci. 41, 3537?3567.

Wilczak, J.M. and Tillman, J.E.: 1980, ?The Three-Dimensional Structure of Convection in the Atmospheric Surface Layer?,J. Atmos. Sci. 37, 2424?2443.

Williams, A.G. and Hacker, J.M.: 1992, ?The Composite Shape and Structure of Coherent Eddies in the Convective Boundary Layer?,Boundary-Layer Meteorol. 61, 213?245.

Wippermann, F., Etling, D. and Kirstein, H.J.: 1978, ?On the Instability of a Planetary Boundary Layer with Rossby-Number Similarity. Part II: The Combined Effect of Inflection Point Instability and Convective Instability?Boundary-Layer Meteorol. 15, 301?321.

Wyngaard, J.C. and Brost, R.A.: 1984, ?Top-Down and Bottom-Up Diffusion of a Scalar in the Convective Boundary Layer?,J. Atmos. Sci. 41, 102?112.

Young, G.S.: 1988, ?Turbulence Structure of the Convective Boundary Layer. Part II: Phoenix 78 Aircraft Observations of Thermals and Their Environment?,J. Atmos. Sci. 45, 727?735.

Zivkovic, M. and Agee, E.M.: 1988, ?Further Aspects of Transitions in Two-Dimensional Thermal Convection?,J. Atmos. Sci. 45, 3983?3995.