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Boltzmann-Jaynes variational method and the temperature distribution of thermals in the turbulent convective atmospheric surface layer

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Abstract

A statistical mechanism that explains the formation of probability distribution functions of thermals according to temperature fluctuations is considered. In the proposed approach based on the Boltzmann-Jaynes variational method, a statistical ensemble of convective thermals is characterized by a class of stationary probability densities that depend on temperature fluctuations. It is assumed that the probability density functions of this class may depend on the potential energy, as well as on the available potential energy. For a class of stationary probability density functions, the entropy functional is defined to be an analogue of the Boltzmann H-entropy. The equilibrium distributions of thermals according to temperature fluctuations correspond to the most probable distributions that yield a maximum of the entropy functional. The exponential and normal distributions of thermals according to temperature fluctuation that are constructed using the variational method quite adequately approximate field atmospheric observations, as well as the results of laboratory modeling.

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References

  1. R. S. Scorer and F. H. Ludlam, “Bubble Theory of Penetrative Convection,” Quart. J. Roy. Metor. Soc 79(339), 94–106 (1953).

    Article  Google Scholar 

  2. W. P. Hooper and J. E. James, “Lidar Observation of Ship Spray Plumes,” J. Atmos. Sci. 57(16), 2649–2655 (2000).

    Article  Google Scholar 

  3. O. Taconet and A. Weill, “Convective Plumes in the Atmospheric Boundary Layer as Observed with an Acoustic Doppler Sodar,” Bound. Layer Meteorol. 25(2), 143–158 (1983).

    Article  Google Scholar 

  4. E. M. Sparow, R. B. Husar, and R. J. Goldstein, “Observation and Other Characteristics of Thermals,” J. Fluid Mech. 41, 793–800 (1970).

    Article  Google Scholar 

  5. N. I. Vulfson, Study of Convective Motions in a Free Atmosphere (Izdatel’stvo AN SSSR, Moscow, 1961); N. I. Vulfson, Convective Motions in a Free Atmosphere. Program for Scientific Translation (Jerusalem-Washington, 1964).

    Google Scholar 

  6. D. H. Lenschow and P. L. Stephens, “The Role of Thermals in the Convective Boundary Layer,” Bound. Layer Meteorol., 19(4), 509–532 (1980).

    Article  Google Scholar 

  7. M. J. Manton, “On the Structure of Convection,” Bound. Layer Meteorol. 12(4), 491–509 (1977).

    Article  Google Scholar 

  8. A. N. Vulfson and O. O. Borodin, “Boltzmann Statistical Theory and Asymptotics of the Temperature Distribution of Spontaneous Jets in the Convective Atmospheric Surface Layer,” Izv., Atmos. Ocean. Phys. 44(6), 723–728 (2008).

    Article  Google Scholar 

  9. D. H. Lenschow, “Airplane Measurement of Planetary Boundary Layer Structure,” J. Appl. Meteorol. 9(6), 874–884 (1970).

    Article  Google Scholar 

  10. B. M. Koprov, S. L. Zubkovsky, V. M. Koprov, et al., “Statistics of Air Temperature Spatial Variability in the Atmospheric Surface Layer,” Bound. Layer Meteorol. 88(3), 399–423 (1998).

    Article  Google Scholar 

  11. L. Boltzmann, “Über die Beziehung zwischen dem zweiten Hauptsatze der Mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, respective den Sätzen über das das Wärmegleichgewicht,” Wien. Akad. Sitzungsber 76, 373–435 (1878); L. Boltzmann, “On the Relationship between the Second Main Theorem of Mechanical Heat Theory and the Probability Calculation with respect to the Results on the Heat Equilibrium,” in Selected Works (Nauka, Moscow, 1984), pp. 190–241.

    Google Scholar 

  12. E. T. Jaynes, “Information Theory and Statistical Mechanics,” Phys. Rev. 106(4), 620–630 (1957).

    Article  Google Scholar 

  13. A. S. Frish and J. A. Businger, “A Study of Convective Elements in the Atmospheric Surface Layer,” Bound. Layer Meteorol. 3, 301–328 (1973).

    Article  Google Scholar 

  14. S.-C. Lin, L. Tsang, and C. P. Wang, “Temperature Field Structure in Strongly Heated Buoyant Thermals,” Phys. Fluids 15(12), 2118–2128 (1972).

    Article  Google Scholar 

  15. R. S. Schechter, The Variational Method in Engineering (McGraw Hill, New York—London-Sydney, 1967; Mir, Moscow, 1971).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Oil and Gas Problems, Russian Academy of Sciences, ul. Gubkina 3, Moscow, 117701, Russia

    A. N. Vul’fson & O. O. Borodin

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  1. A. N. Vul’fson
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  2. O. O. Borodin
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Correspondence to A. N. Vul’fson.

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Original Russian Text © A.N. Vul’fson, O.O. Borodin, 2012, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2012, Vol. 48, No. 6, pp. 674–681.

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Vul’fson, A.N., Borodin, O.O. Boltzmann-Jaynes variational method and the temperature distribution of thermals in the turbulent convective atmospheric surface layer. Izv. Atmos. Ocean. Phys. 48, 603–609 (2012). https://doi.org/10.1134/S0001433812050118

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  • DOI: https://doi.org/10.1134/S0001433812050118

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