Field Evolution Within the Framework of the Burgers Equation

  • S. N. Gurbatov
  • O. V. Rudenko
  • A. I. Saichev
Part of the Nonlinear Physical Science book series (NPS)


In this chapter, we describe some solutions of the Burgers equation for single-scale fields, discuss properties of solutions to the Burgers equation for multi-scale fields, which, in one way or another, help to understand laws of evolution of noise fields.


Heavy Particle Burger Equation Field Evolution Linear Stage Integral Length Scale 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O.V. Rudenko. S.N. Gurbatov, CM. Hedberg, Nonlinear Acoustics through Problems and Examples (Trafford, 2010)Google Scholar
  2. 2.
    O.V. Rudenko, S.I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Plenum, New York, 1977)MATHGoogle Scholar
  3. 3.
    S.N. Gurbatov, D.B. Crighton, The nonlinear decay of complex signals in dissipative media, Chaos 5, 524–530 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    J.R. Angilella, J.C. Vassilicos, Speclral, diffusive and convective properlies of fractal and spiral fields, Physica D 124, 23–57 (1998)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    J.M. Burgers, The Nonlinear Diffusion Equation (D. Rcidel, Dordrecht, 1974)MATHGoogle Scholar
  6. 6.
    U. Frisch, ’Turbulence: the Legacy of A.N. Kolmogorov (Cambridge University Press, 1995)Google Scholar
  7. 7.
    S. Kida, Asymptotic properties of Burgers turbulence, J. Fluid Mech. 93, 337–377 (1979)MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    S.A. Molchanov, D. Surgailis. W.A. Woyczynski, Hyperbolic asymptotics in Burgers’ turbulence and extremal processes, Comm. Math. Phys. 168, 209–226 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    S.N. Gurbatov, A.N. Malakhov, A.I. Saichev, Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves. Rays andParticles. (Manchester University Press, 1991)Google Scholar
  10. 10.
    S.N. Gurbatov, A.V. Troussov, The decay of multiscale signals — deterministic model of the Burgers turbulence, Phys. D 145, 47–64 (2000)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    H. Aurell, S.N. Gurbalov, I.I. Wertgeim, Self-preservation of large-scale structures in Burgers turbulence, Phys. Lett. A 182, 109–113 (1993)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    S.N. Gurbatov, G.V. Pasmanik, Self-preservation of large-scale structures in a nonlinear viscous medium described by the Burgers equation. J. Exp. Theoret. Phys. 88, 309–319 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    S.N. Gurbatov, A.I. Saichev, Degeneracy of one-dimensional acoustic turbulence at large Reynolds numbers, Sov. Phys. JETP 80, 589–595 (1981)Google Scholar
  14. 14.
    M.V. Berry, Z.V. Lewis, On the Weierstrass—Mandelbrot fractal function, Proc. Roy. Soc. A 340, 459–484 (1980)MathSciNetADSGoogle Scholar
  15. 15.
    B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1982)MATHGoogle Scholar
  16. 16.
    M. Vergassola, B. Dubrulle, U. Frisch, A. Noullez, Burgers’ equation, devil’s staircases and the mass distribution for large-scale structures, Astron. Astrophys. 289, 325–356 (1994)ADSGoogle Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • S. N. Gurbatov
    • 1
  • O. V. Rudenko
    • 2
  • A. I. Saichev
    • 3
  1. 1.Radiophysics DepartmentNizhny Novgorod State UniversityNizhny NovgorodRussia
  2. 2.Physics DepartmentMoscow State UniversityMoscowRussia
  3. 3.Radiophysics DepartmentNizhny Novgorod State UniversityNizhny NovgorodRussia

Personalised recommendations