ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa


Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2011, Vol. 8, No. 3, pp. 251-256

The analysis of structure properties of electric turbulence in thunderstorm clouds

N.S. Erokhin 1, N.N. Zolnikova 1, I.A. Krasnova 2, L.A. Mikhailovskaya 1
1 Space Research Institute of RAS, 117997, Moscow, 84/32, Profsoyuznaya str
2 People Friendship University of Russia, 115419, Москва, ул. Орджоникидзе, д.3
It has been performed the numerical analysis of structure functions Sm(L) for an electric turbulence in thunderclouds by usage of experimental data on altitude profile of the electric field vertical component E(z) in the height range up to 13 km. Digitization of the experimental plots and development of analytical approximations Ea(z) for the electric field E(z) in thunderstorm clouds in a class of localized functions were made. Numerical calculations of the structure functions Sm(L) for the orders m in the range 0.1 ≤ m ≤ 7 were performed with small enough step in the altitude δz = 1 m. Plots of Sm(L) have been obtained and inertial intervals (where power law degree dependence of Sm(L) is observing) of electric turbulence were detected in the small scales range and the middle scale one. Scaling exponents g(m) for inertial intervals were determined which are significantly differ from the Kolmogorov scaling gk(m) = m / 3 and the helical one gh(m) = 2 m / 3 in the homogeneous, isotropic hydrodynamical turbulence. It is established that Sm(L) behaviour may be explained by presence in middle scale range of intermittency and coherent structures which influence on scaling exponents g(m). Results obtained are of the great interest for following investigations of intense atmospheric vortices charged subsystems contribution to the hydrodynamical helicity H = V rot V generation and to the development of inhomogeneous, self-consistent wind structure in the vortice.
Keywords: structure functions, inertial intervals, electric turbulence, scaling exponents, thunderstorm clouds, coherent structures, altitude distributions
Full text


  1. Erokhin N.S., Moiseev S.S., Problemy geofiziki XXI veka (Problems of Geophysics of the XXI century), Moscow: Nauka, 2003, Vol. 1, 160 p.
  2. Krasnova I.A., Erokhin N.S., XLVI Vserossiiskaya Konferentsiya po Problemam Matematiki, Informatiki, Fiziki i Khimii (XLVI All-Russian Conference on Problems of Mathematics, Informatics, Physics and Chemistry), Moscow: RUDN, Tezisy dokladov (Abstracts), 2010, p. 17.
  3. Moiseev S.S., Chkhetiani O.G., ZhETF, 1996, Vol. 110, Issue 1 (7), p. 357.
  4. Arteha S.N., Golbraikh E., Erokhin N.S., Problems of Atomic Science and Technique, 2003, No. 4, p. 94.
  5. Branover H, Eidelman A., Golbaikh E., Moiseev S., Turbulence and Structures. Chaos, Fluctuations and Self-organization in Nature and in the Laboratory, San-Diego, Academic Press, 1998, 270 p.
  6. Byrne G.J., Few A.A., Stewart M.F., Journal of Geophysical Research, 1989, Vol. 94, No. D5, p. 6297.
  7. Horbury T.S., Balogh A., Nonlinear Processes in Geophysics, 1997, Vol. 4, No. 3, p. 185.
  8. Lazarev A.A., Moiseev S.S., Geophysical Precursors of Early Stages of Cyclogenesis, Preprint IKI RAS, Pr–1844, 1990.
  9. Litvinenko L.N., Ryabov V.B., Usik P.V. et al., Correlation Dimension: The New Tool in Astrophysics, Institute of Radio Astronomy, Academy of Sciences of Ukraine, Preprint No. 64, Kharkov, 1992, 53 p.
  10. Marsh E., Tu C.Y., Nonlinear Processes in Geophysics, 1997, Vol. 4, No. 1, p. 101.
  11. Marshak A., Davis A., Wiscombe W., Cahalan R., Journal of Atmospherical Sciences, 1997, Vol. 54, No. 11, pp. 1423-1444.
  12. Marshall T.C., Rust W.D., Journal of Geophysical Research, 1995, Vol. 100, p. 1001.
  13. Osborne A.R., Provenzale A., Physica D, 1989, Vol. 35, No. 2, p. 357.
  14. Schertzer D., Lovejoy S., Schmitt F., Chigirinskaya Y., Marsan D., Fractals, 1997, Vol. 5, No. 3, pp. 427-471.