Analysis of the fractal structures in turbulent processes

Authors: A.A.Svinarenko, O.Yu. Khetselius, V.F.Mansarliysky, S.I. Romanenko

Year: 2014

Issue: 15

Pages: 74-78


On the basis of wavelet analysis and multifractal formalism it is carried out an analysis of fractal structures in the turbulent processes (parietal pressure pulsations in a turbulent flow in the pipe).

Tags: fractals structures; turbulent processes


  1. Mandelbrot B. Fractal geometry of nature.- M.: Mir.-2002.
  2. Schertzer D., Lovejoy S. Fractals: Physical Origin and Properites, Ed. Peitronero L.-N.-Y.: Plenum Press.-1990.-P.71-92.
  3. Sprott J.C., Vano J.A., Wildenberg J.C., Anderson M.B., Noel J.K. Coexistence and chaos in complex ecologies // Phys. Lett. A.-2005.-V.335, № 2-3.-P.207-212.
  4. Zaslavsky G.M. Stochasticity of dynamical systems.- Moscow: Nauka.-1998.
  5. Zosimov V.V., Lyamshev L.M. Fractals in wave processes //Phys.Uspekhi.-1995.-Vol.165.-P.361–402.
  6. Rabinovich M.I., Sushchik M.M. Regular and chaotic dynamics of structures in flows of a liquid//Phys.Uspekhi.-1990.-Vol.160.-P.3–64.
  7. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors// Physica D. – 1983. – Vol. 9. – P. 189-208.
  8. Kaplan J.L., Yorke J.A. Chaotic behavior of multidimensional difference equations // Functional differential equations and approximations of fixed points. Lecture Notes in Mathematics No. 730 / H.-O. Peitgen, H.-O. Walter (Eds.). – Berlin: Springer, 1979. – P. 204-227.
  9. Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series// Phys. Rev. Lett.-1980.-Vol.45.-P.712-716.
  10. Schreiber T. Interdisciplinary application of nonlinear time series methods//Phys. Rep.-1999.-Vol.308.-P.1-64.
  11. Svinarenko A.A. Regular and chaotic dynamics of multi-oscillator dynamical systems// Photoelectronics.-2002.-Vol.11.-P.81-84.
  12. Daubechies I. Ten Lectures on Wavelets.- Philadelphia: SIAM.- 1992.
  13. Morlet J., Arens G., Fourgeau E. and Giard D. Wave propagation and sampling theory// Geophysics.-1982.-Vol.47.-p.203-236.
  14. Nason G., von Sachs R., Kroisand G. Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum // J.Royal Stat.Soc. -2000.-Vol.B62.-P.271-292.
  15. Glushkov A.V., Khokhlov V.N., Svinarenko A.A., Bunyakova Yu.Ya., Prepelitsa G.P. Wavelet analysis and sensing the total ozone content in the earth atmosphere: Mycros technology “Geomath”//Sensor Electr. and Microsys.Techn.-2005.-Vol.2(3).-P.51-60.
  16. Glushkov A.V., Khokhlov V.N., Tsenenko I.A. Atmospheric teleconnection patterns: wavelet analysis// Nonlin. Geophys.-2004.-V.11,N3.-P.285-293.
  17. Khokhlov V.N., Glushkov A.V., Loboda N.S., Bunyakova Yu.Ya. Short-range forecast of atmospheric pollutants using non-linear prediction method// Atmospheric Environment (Elsevier).-2008.-Vol.42.-P. 7284–7292.
  18. Glushkov A.V., Loboda N.S., Khokhlov V.N., Lovett L. Using non-decimated wavelet decomposition to analyse time variations of North Atlantic Oscillation, eddy kinetic energy, and Ukrainian precipitation // Journal of Hydrology (Elsevier).-2006.-Vol. 322,N1-4.-P.14-24.
  19. Akimov V.G., Zosimov V.V., Sushkov A.L. Multifractal structure of the near-wall intermittency of turbulent fluctuations of pressure in the pipe //Acoust.Journ..–1992. – Vol.38(2).-P.375–378.
  20. Meneveau C., Sreenivasan K.R. Simple multifractal cascade model for fully developed turbulence//Phys. Rev. Lett.-1987.-Vol.59.-P.1424-1428.
  21. Sivakumar B. Chaos theory in geophysics: past, present and future // Chaos, Solitons & Fractals.-2004.-Vol.19.-P.441-462.
Download full text (PDF)