Abstract
A new mean-field theory of turbulent convection is developed based on the idea that only the small-scale region of the spectrum is considered as turbulence, whereas its large-scale part, including both regular and semi-organized motions, is treated as the mean flow. In the shear-free regime, this theory predicts the convective wind instability, which causes the formation of large-scale semi-organized motions in the form of cells. In the presence of wind shear, the theory predicts another type of instability, which causes the formation of large-scale semi-organized structures in the form of rolls and the generation of convective-shear waves propagating perpendicular to the convective rolls. The spatial characteristics of these structures, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This theory might be useful for understanding the origin of large-scale cells and rolls observed in the convective boundary layer and laboratory turbulent convection
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References
Alpers W. and Brümmer B. (1994). ‘Atmospheric Boundary Layer Rolls Observed by the Synthetic Aperture Radar Aboard the ERS-1 Satellite’. J. Geophys. Res 99(C6):12613–12621
Asai T. (1970). ‘Stability of a Plane Parallel Flow with Variable Vertical Shear and Unstable Stratification’. J. Meteorol. Soc. Japan 48:129–139
Atkinson B.W. and Wu Zhang J. (1996). ‘Mesoscale Shallow Convection in the Atmosphere’. Rev. Geophys. 34:403–431
Brooks I.M. and Rogers D.P. (1997). ‘Aircraft Observations of Boundary Layer Rolls off the Coast of California’. J. Atmos. Sci 54:1834–1849
Brümmer B. (1999). ‘Roll and Cell Convection in Winter-Time Arctic Cold-Air Outbreaks’. J. Atmos. Sci 56:2613–2636
Canuto V.M., Minotti F., Ronchi C., Ypma R.M., and Zeman O. (1994). ‘Second-Order Closure PBL Model with New Third-Order Moments: Comparison with LES’. J. Atmos. Sci 51:1605–1618
Chlond A. (1992). ‘Three-Dimensional Simulation of Cloud Street Development during a Cold Air Outbreak’. Boundary-Layer Meteorol 58:161–200
Elperin, T., Kleeorin, N., Rogachevskii, I., and Zilitinkevich, S.: 2002, ‘Formation of Large-Scale Semi-Organized Structures in Turbulent Convection’. Phys. Rev. E 66:066305 (1–15)
Etling D. (1985). ‘Some Aspects on Helicity in Atmospheric Flows’. Contrib. Atmos. Phys. 58:88–100
Etling D. and Brown R.A. (1993). ‘Roll Vortices in the Planetary Boundary Layer: A Review’. Boundary-Layer Meteorol 65:215–248
Garratt J.R. (1992). The Atmospheric Boundary Layer. Cambridge University Press, U.K., 316 pp
Hunt J.C.R. (1984). ‘Turbulence Structure in Thermal Convection and Shear-Free Boundary Layers’. J. Fluid Mech 138:161–184
Hunt J.C.R., Kaimal J.C., and Gaynor J.I. (1988). ‘Eddy Structure in the Convective Boundary Layer – New Measurements and New Concepts’. Quart. J. Roy. Meteorol. Soc 114:837–858
Kadanoff L.P. (2001). ‘Turbulent Heat Flow: Structures and Scaling’. Phys. Today 54:34–38
Kaimal J.C. and Fennigan J.J. (1994). Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, Oxford, 289 pp
Kaimal J.C., Wyngaard J.C., Haugen D.A., Cote O.R., and Izumi Y. (1976). ‘Turbulence Structure in the Convective Boundary Layer’. J. Atmos. Sci 33:2152–2169
Krishnamurti R. and Howard L.N. (1981). ‘Large-Scale Flow Generation in Turbulent Convection’. Proc. Natl. Acad. Sci. USA 78:1981–1985
Lenschow D.H. and Stephens P.L. (1980). ‘The Role of Thermals in the Convective Boundary Layer’. Boundary-Layer Meteorol 19:509–532
Lumley J.L. (1967). ‘Rational approach to Relations between Motions of Different Scales in Turbulent Flows’. Phys. Fluids 10:1405–1408
Mahrt L. (1991). ‘Eddy Asymmetry in the Sheared Heated Boundary Layer’. J. Atmos. Sci 48:472–492
Mason P.J. (1985). ‘A Numerical Study of Cloud Street in the Planetary Boundary Layer’. Boundary-Layer Meteorol 32:281–304
McComb W.D. (1990). The Physics of Fluid Turbulence. Clarendon Press, Oxford, 572 pp
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. and Wyngaard J.C. (1984). ‘Statistics of Conservative Scalars in the Convective Boundary Layer’. J. Atmos. Sci 41:3161–3169
Moeng C.-H. and Wyngaard J.C. (1989). ‘Evaluation of Turbulent Transport and Dissipation Closures in Second-Order Modelling’. J. Atmos. Sci 46:2311–2330
Monin A.S. and Yaglom A.M. (1975). Statistical Fluid Mechanics. MIT Press, Cambridge Massachusetts, Vol. 2, 874 pp
Niemela J.J., Skrbek L., Sreenivasan K.R., and Donnelly R.J. (2001). ‘The Wind in Confined Thermal Convection’. J. Fluid Mech 449:169–178
Orszag S.A. (1970). ‘Analytical Theories of Turbulence’. J. Fluid Mech 41:363–386
Pouquet A., Frisch U., and Leorat J. (1976). ‘Strong MHD Turbulence and the Nonlinear Dynamo Effect’. J. Fluid Mech 77:321–354
Robinson S.K. (1991). ‘Coherent Motions in the Turbulent Boundary Layer’. Annu. Rev. Fluid Mech 23:601–640
Schmidt H. and Schumann U. (1989). ‘Coherent Structure in the Convective Boundary Layer Derived from Large-Eddy Simulations’. J. Fluid Mech 200:511–562
Shirer H.N. (1986). ‘On Cloud Street Development in Three Dimensions: Parallel and Rayleigh Instabilities’. Contrib. Atmos. Phys 59:126–149
Stensrud D.J. and Shirer H.N. (1988). ‘Development of Boundary Layer Rolls from Dynamical Instabilities’. J. Atmos. Sci 45:1007–1019
Stull R.B. (1988). An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, 666 pp
Sykes R.I. and Henn D.C. (1989). ‘Large-Eddy Simulation of Turbulent Sheared Convection’. J. Atmos. Sci 46:1106–1118
Weckwerth T.M., Horst T.W., and Wilson J.W. (1999). ‘An Observational Study of the Evolution of Horizontal Convective rolls’. Mon. Wea. Rev 127:2160–2179
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
Williams A.G. and Hacker J.M. (1993). ‘Interaction between Coherent Eddies in the Lower Convective Boundary Layer’. Boundary-Layer Meteorol 64:55–74
Wyngaard J.C. (1983). ‘Lectures on the Planetary Boundary Layer’. In: Lilly D.K. and Gal-Chen T (eds). Mesoscale Meteorology – Theories, Observations and Models. Reidel, Dordrecht, pp. 603–650
Wyngaard J.C. (1987). ‘A Physical Mechanism for the Asymmetry in Top-Down and Bottom-Up Diffusion’. J. Atmos. Sci 44:1083–1087
Wyngaard J.C. (1992). ‘Atmospheric Turbulence’. Annu. Rev. Fluid Mech 24:205–233
Young G.S., Kristovich D.A.R., Hjelmfelt M.R., and Foster R.C. (2002). ‘Rolls, Streets, Waves and More’. Bull. Amer. Meteorol. Soc 83:997–1001
Zeman O. and Lumley J.L. (1976). ‘Modeling Buoyancy Driven Mixed Layers’. J. Atmos. Sci 33:1974–1988
Zilitinkevich, S. S.: 1991. Turbulent Penetrative Convection:Avebury Technical, Aldershot, 179 pp
Zilitinkevich S.S., Grachev A., and Hunt J.C.R. (1998). ‘Surface Frictional Processes and Non-Local Heat/Mass Transfer in the Shear-Free Convective Boundary Layer’. In: Plate E.G. et al. (eds). Buoyant Convection in Geophysical Flows. Kluwer Academic Publications, Dordrecht, The Netherlands, pp. 83–113
Zilitinkevich S.S., Gryanik V.M., Lykossov V.N., and Mironov D.V. (1999). ‘Third-Order Transport and Nonlocal Turbulence Closures for Convective Boundary Layers’. J. Atmos. Sci 56:3463–3477
Zocchi G., Moses E., and Libchaber A. (1990). ‘Coherent Structures in Turbulent Convection’. Physica A 166:387–407
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Elperin, T., Kleeorin, N., Rogachevskii, I. et al. Tangling Turbulence and Semi-Organized Structures in Convective Boundary Layers. Boundary-Layer Meteorol 119, 449–472 (2006). https://doi.org/10.1007/s10546-005-9041-5
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DOI: https://doi.org/10.1007/s10546-005-9041-5