Fractal properties of the aerpolectric field
Category: 16-4UDC 551.594.1
S.V. Anisimov, N.M. Shikhova
Borok Geophysical Observatory of Schmidt Institute of Physics of the Earth of the Russian Academy of Science, Borok (Yaroslavl region), Russia
Abstract. The regularities of the daily dynamics of scaling (fractal dimension, Hurst exponent) and power (spectral slope and structural functions exponents) characteristics of the terrestrial atmosphere at various states are revealed using observational data. The scaling properties and the presence of intermittency in the dynamics of the aeroelectric field in the unperturbed surface atmosphere are investigated. It is shown that in frequency range 0.001 to 1 Hz, aeroelectric pulsations display self-similarity properties with a fractal dimension D=1.1–1.8. Time intervals characterized by the change of the stratification in the surface atmosphere with intermittency properties are detected.
It is shown that the intermittency of the aeroelectric field is characterized by a non-Gaussian distribution of the field increments, the change in spectral density slope from –2.3 to –4, and the multifractal spectrum with a width significantly different from zero in the frequency range of 0.01–1 Hz. The methods for quantitative diagnostics of the homogeneity and isotropy of short-period aeroelectric pulsations are proposed.
Keywords: atmospheric electricity, aeroelectric field, multifractal analysis, turbulence, intermittency, scaling.
References
Anisimov S. V., Afinogenov K. V., and ShikhovaN. M.Dynamics of undisturbed midlatitude atmospheric from observations to scaling. Radiophysics and Quantum Electronics, 2014, vol. 56, nos. 11–12, pp. 709 – 722.
Anisimov S. V., Galichenko S. V., ShikhovaN. M., and Afinogenov K. V. Electricity of the Convective Atmospheric Boundary Layer: Field Observations and Numerical Simulation, Izvestiya, Atmospheric and Oceanic Physics, 2014, vol. 50, no. 4, pp. 390–398.
Anisimov S. V., Mareev E. A., Shikhova N. M., Shatalina M. V., Galichenko S. V., and. Zilitinkevich S. S. Aeroelectric structures and turbulence in the atmospheric boundary layer, Nonlin. Processes Geophys., 2013, vol. 20, pp.819–824.
Anisimov S.V., Galichenko S.V., and Shikhova N.M. Formation of electrically active layers in the atmosphere with temperature inversion , Izvestiya, Atmospheric and Oceanic Physics, 2012, vol.48, no. 4, pp.391-400.
Anisimov S.V., Mareev E.A, Shikhova N.M., and Dmitriev E.M. Universal spectra of electric field pulsations in the atmosphere, Geophys. Res. Letters, 2002, vol. 29, no. 24, 2002GL015765.
Anisimov S.V. and Mareev E.A. Aeroelectrical structures in atmosphere, Doklady of the Russian Academy of Sciences, 2000, vol. 371, no.1, pp. 101 –104.
Anisimov S.V. and Shikhova N.M. Intermittency of turbulent aeroelectric field, Atmospheric Research, 2014, vol. 135–136, p.255–262, dx.doi.org/10.1016/j.atmosres.2012.12.018.
Anisimov S.V., Shikhova N.M., Mareev E.A., and Shatalina M.V.Structure functions and spectra of turbulent fluctuations in the aeroelectric field, Izvestiya, Atmospheric and Oceanic Physics, 2003, vol.39, no. 6, pp.690-704.
Anisimov, S.V., Mareev E.A., and Bakastov S.S.On the generation and evolution of aeroelectric structures in the surface layer, J. Geophys. Res., 1999, vol. 104, no.D12, pp. 14359-14367.
Budaev V. P., S. Savin, L. Zelenyi, N. Ohno, S. Takamura, and E. Amata. Intermittency and extended self-similarity in space and fusion plasma: boundary effects, Plasma Phys. Control Fusion, 2008. doi:10.1088/0741-3335/50/7/074014.
Budaev, V.P., Savin, S.P., and Zelenyi, L.M.,Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition ofplasma transport features, Physics-Uspekhi,2011, vol.54, no.9, pp. 875–918.
Chkhetiani O.G., Eidelman A., and Golbraikh E. Large- and small-scale turbulent spectra in MHD and atmospheric flows, Nonlin. Processes Geophys., 2006, vol.13, no.6, pp. 613–620.
Crownover R. M. Introduction to fractals and chaos. Jones and Bartlett. Mathematics 1995, 306 p.
Erokhin N.S. , Zolnikova N.N. , Krasnova I.A., and MikhailovskayaL.A. The analysis of structure properties of electric turbulence in thunderstorm clouds, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2011, vol. 8, no. 3, pp. 251-256.
Feder, J., Fractals, Plenum Press, New York 1988, 283p.
Flandrin P. On the Spectrum of Fractional Brownian Motions, IEEE Transactions on Information Theory. 1989, vol. 35, no. 1, pp.197-199.
Frick P.G. Turbulence: Approaches and Models. 2-nd Edition. М.; Izhevsk: RDC “Regular and Chaotic Dynamics”, 2010. 332 p.
Frisch U. Turbulence. The legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge, 1995, 296 p.
Gelashvili D. B., Iudin D. I., Rozenberg G. S., Yakimov V. N., and Solntsev L. A. Fractals and Multifractals in Bioecology. N. Novgorod: Univ. Press, 2013, 370 p.
Gordienko S.N. and Moiseev S.S.On turbulent diffusion of a passive tracer, Technical Physics Letters, 1999, vol.25, no. 7, pp. 51-56.
Hausdorff F. Dimesion und Ausseres Mass, Matematishe Annalen, 1919, no.79, pp. 157-179.
Higuchi T. Approach to an irregular time series on the basis of the fractal theory, Physica D. 1988. vol. 31, no.3, pp. 277–283.
Kolmogorov, A.N. Local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers, Dokl. Akad. Nauk SSSR, 1941, vol. 30, no.4, pp. 299–303.
Lyubushin A. A. Mapping the Properties of Low-Frequency Microseisms for Seismic Hazard Assessment,Izvestiya, Physics of the Solid Earth, 2013, vol.49, no.1, pp. 9-18.
Lyubushin A.A. Exploratory analysis of the properties of time series based on the use of interactive program Spectra_Analyzer in: Textbook for senior courses geophysical faculty. Мoscow: RSGSU, 2006, 46 p.
Lyubushin A.A. Geophysical Monitoring Data Analysis, Мoscow: Nauka, 2007, 228 p.
Mahrt, L. and Vickers D. Extremely weak mixing in stable conditions, Bound.-Layer Meteor. 2006, vol. 119, no. 1, pp. 19-39.
Mandelbrot B.B. and van Ness J.W. Fractional Brownian motions, fractional noises and applications, SIAM Review,1968. vol.10, no. 4, pp. 422-437.
Mandelbrot В.В. The Fractal Geometry of Nature, San-Francisco: Freeman, 1982, 460p.
Muzy J.F., Bacry E., and Arneodo A. Wavelets and multifractal formalism for singular signals: application to turbulence data, Phys. Rev. Lett., 1991, vol.67, pp. 3515–3518.
Ostanin S. A. and Shaiduk A. M.Improving of the accuracy of the relationship between fractal dimension and the index of the power spectrum of the signal, Journal of radio electronics, 2012. no 8, jre.cplire.ru/koi/aug12/5/text.pdf.
Parisi, G. and Frisch, U. On the singularity structure of fully developed turbulence, in Turbulence and Predictability in Geophysical Fluid Dynamics, edited by Ghil, M., Benzi, R., and Parisi, G., North-Holland, Amsterdam, 1985, pp. 84–87.
Pavlov A. N. and Anishchenko V. S. Multifractal analysis of complex signals, Physics-Uspekhi, 2007, vol. 50, no. 8, pp. 819–834.
Schroeder M.R. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. Courier Corporation, 2012, 429 p.
Sorbjan Z. Local structure of turbulence in stably stratified boundary layers, J. Atmos. Sci., 2006, vol.63, no. 5, pp. 1526-1537.
Zakharov V. E., Vasilyev O. A., Dyachenko, and A. I. Kolmogorov spectra in one-dimensional weak turbulence, Journal of Experimental and Theoretical Physics Letters,2001, vol.73, no. 2,pp. 68–70.
Zelenyi L. M. and Milovanov A. V. Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics.