, Volume 60, Issue 3, pp 408–421 | Cite as

Diffusion of Radiation in Inhomogeneous Turbulent Atmospheres

  • A. G. Nikoghossian

The model problem of the formation of spectral lines in an absorbing and scattering atmosphere of finite optical depth with developed turbulence is stated and solved. The purpose of this paper is to clarify the influence of different kinds of spatial correlated nonthermal motions on observed line profiles. The method of invariant imbedding is used; it enables solution of this problem under rather general assumptions about the character of the turbulence, as well as about elementary scattering events and the distribution of energy sources in the medium. Special attention is devoted to the limits of macro- and microturbulence. It is shown that in the case of microturbulence, the reflectivity of the medium and its opacity are greater over the entire frequency range. It is also found that the dependence of the observed characteristics on the correlation length is stronger when medium is thicker and the average velocity of the turbulent motions is higher.


radiative transfer: turbulent atmosphere: correlation length 


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  1. 1.
    D. F. Gray, Sol. Phys. 59, 193 (1978).ADSCrossRefGoogle Scholar
  2. 2.
    A. G. Nikoghossian, Astrofizika 50, 219 (2007), [Astrophysics, 50, 175 (2007)].Google Scholar
  3. 3.
    M. Auvergne, H. Frish, Ch. Froeschle, and A. Pouquet, Astron. Astrophys. 29, 93 (1973).ADSGoogle Scholar
  4. 4.
    H. Frish, Astron. Astrophys. 40, 267 (1975).ADSGoogle Scholar
  5. 5.
    H. Frish and U. Frish, Mon. Not. Roy. Astron. Soc. 175, 157 (1976).ADSCrossRefGoogle Scholar
  6. 6.
    H. P. Gail and E. Sedlmayr, Astron. Astrophys. 36, 17 (1974).ADSGoogle Scholar
  7. 7.
    H. P. Gail, E. Sedlmayr, and G. Traving, Astron. Astrophys. 44, 421 (1975).ADSGoogle Scholar
  8. 8.
    E. Hundt, Astron. Astrophys. 29, 17 (1973).ADSGoogle Scholar
  9. 9.
    A. G. Nikoghossian, Astrofizika 50, 321 (2007), [Astrophysics, 50, 391 (2007)].Google Scholar
  10. 10.
    A. G. Nikoghossian, Light Scat. Rev. 8, 425 (2013).Google Scholar
  11. 11.
    C. Magnan, J. Quant. Spectrosc. Radiat. Transfer 15, 979 (1975).ADSCrossRefGoogle Scholar
  12. 12.
    E. S. Ventsel’, Probability Theory [in Russian], Nauka, Moscow (1964).Google Scholar
  13. 13.
    G. Batchelor, The Theory of Homogeneous Turbulence, Cambridge, Cambridge Univ. Press. 1970).MATHGoogle Scholar
  14. 14.
    A. T. Bharucha-Reid, Elements of the Theory of Markov Processes and Their Applications, New York, McGraw-Hill (1960).MATHGoogle Scholar
  15. 15.
    M. S. Bartlett, An Introduction to Stochastic Processes, Cambridge Univ. Press (1965).Google Scholar
  16. 16.
    R. Bellman, R. Kalaba, and M. Wing, J. Math. Phys. 1, 280 (1960).ADSCrossRefGoogle Scholar
  17. 17.
    R. Bellman, R. Kalaba, and M. Prestrud, Invariant Imbedding and Radiative Transfer in Slabs of Finite Thickness, Amer. Elsevier (1963).Google Scholar
  18. 18.
    J. Casti and R. Kalaba, Imbedding Methods in Applied Mathematics [Russian translation], Mir, Moscow (1976).MATHGoogle Scholar
  19. 19.
    A. G. Nikoghossian, Astrofizika 54, 149 (2011), [Astrophysics, 54, 126 (2011)].Google Scholar
  20. 20.
    A. G. Nikoghossian, Astrofizika 57, 296 (2014), [Astrophysics, 57, 272,2014)].Google Scholar
  21. 21.
    A. G. Nikoghossian, Astrofizika 57, 407 (2014), [Astrophysics, 57, 375 (2014)].Google Scholar

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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.V. A. Ambartsumyan Byurakan Astrophysical ObservatoryByurakanArmenia

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