Meteorology and Atmospheric Physics

, Volume 127, Issue 4, pp 451–455 | Cite as

Two-dimensional analytical model of dry air thermal convection

Original Paper


In the present work, the steady-state stationary dry air thermal convection in a lower atmosphere has been studied theoretically. The thermal convection was considered without accounting for the Coriolis force, and with only the vertical temperature gradient. The stream function has been analytically obtained within the framework of two-dimensional thermal convection model in the Boussinesq approximation with velocity divergence taken as zero. It has been shown that the stream function is symmetrical about the horizontal and vertical. The expressions for the horizontal and vertical air velocity components have been obtained. The maximal vertical velocities level is in the center of the convective cell where the horizontal air velocity component is equal to zero. It has been shown that the air parcel’s rotation period during the thermal convection is determined by the Brunt–Väisälä frequency. The expression for the maximal air velocity vertical component has been found. The dependence of the maximal air velocity vertical component on the overheat function at ground surface and on the atmosphere instability has been demonstrated. The expression for the pressure disturbance has been obtained. It has been demonstrated that at the points with maximal pressure disturbance the vertical velocity is equal to zero and the horizontal velocity is maximal. It has been found that the convection cell size depends on the atmosphere stability state.



This work was partially supported by the Ministry of Education and Science of the Russian Federation within the framework of the base part of the governmental ordering for scientific research works (Project No 653).


  1. Alekseev VV, Gusev AM (1983) Free convection in geophysical processes. Sov Phys Usp 26:906–922CrossRefGoogle Scholar
  2. Bluestein HB (2013) Severe convective storms and tornadoes. Springer, ChichesterCrossRefGoogle Scholar
  3. Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Clarendon Press, OxfordGoogle Scholar
  4. Drazin PG (2002) Introduction to hydrodynamic stability. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  5. Emanuel KA (1994) Atmospheric convection. Oxford University Press, New YorkGoogle Scholar
  6. Heavens NG, Richardson MI, Lawson WG, Lee C, McCleese DJ, Kass DM, Kleinböhl A, Schofield JT, Abdou WA, Shirley JH (2010) Convective instability in the martian middle atmosphere. Icarus 208:574–589CrossRefGoogle Scholar
  7. Lambaerts J, Lapeyre G, Zeitlin V (2011) Moist versus dry barotropic instability in a shallow-water model of the atmosphere with moist convection. J Atmos Sci 68:1234–1252CrossRefGoogle Scholar
  8. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141CrossRefGoogle Scholar
  9. Martynenko OG, Khramtsov PP (2005) Free-convective heat transfer. SpringerGoogle Scholar
  10. Monin AS (1990) Theoretical geophysical fluid dynamics. Kluwer Academic Publishers, The NetherlandsCrossRefGoogle Scholar
  11. Ogura Y, Yagihashi A (1971) Non-stationary finite-amplitude convection in a thin fluid layer bounded by a stably stratified region. J Atmos Sci 28:1389–1399CrossRefGoogle Scholar
  12. Pedlosky J (1987) Geophysical fluid dynamics. Springer-VerlagGoogle Scholar
  13. Rayleigh (1916) On convective currents in a horizontal layer of fluid when the higher temperature is on the underside. Phil Mag 32:529–546CrossRefGoogle Scholar
  14. Saltzman B (1962) Finite amplitude free convection as an initial value problem—I. J Atmos Sci 19:329–341CrossRefGoogle Scholar
  15. Sherwood SC, Bony S, Dufresne J-L (2014) Spread in model climate sensitivity traced to atmospheric convective mixing. Nature 505:37–42CrossRefGoogle Scholar
  16. Zdunkowski W, Bott A (2003) Dynamics of the atmosphere: a course in theoretical meteorology. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  • R. G. Zakinyan
    • 1
  • A. R. Zakinyan
    • 1
  • A. A. Lukinov
    • 1
  1. 1.Department of Theoretical Physics, Institute of Mathematics and Natural SciencesNorth Caucasus Federal UniversityStavropolRussian Federation

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