Abstract
For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This means that they are determined by a single rare fluctuation and exhibit an intermittency phenomenon.
Similar content being viewed by others
References
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).
U. Frisch, Turbulence. The Legacy of A. N. Kolmogorov (Cambridge Univ. Press, Cambridge, 1995).
I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Nauka, Moscow, 1982; Wiley, New York, 1988).
K. Efetov, Supersymmetry in Disorder and Chaos (Cambridge Univ. Press, Cambridge, 1997).
A. Z. Patashinskii and V. L. Pokrovskii, Fluctuation Theory of Phase Transitions (Nauka, Moscow, 1982; Pergamon, Oxford, 1979).
V. V. Lebedev, Pis’ma Zh. Éksp. Teor. Fiz. 70, 675 (1999) [JETP Lett. 70, 691 (1999)].
V. V. Lebedev, Phys. Rev. E 62, 1002 (2000).
I. V. Kolokolov, Pis’ma Zh. Éksp. Teor. Fiz. 71, 20 (2000) [JETP Lett. 71, 12 (2000)].
J. M. Burgers, The Nonlinear Diffusion Equation (Reidel, Dordrecht, 1974).
M. Kardar, G. Parisi, and Y. Zhang, Phys. Rev. Lett. 56, 889 (1986).
G. Blatter, M. V. Feigelman, V. B. Geshkenbein, et al., Rev. Mod. Phys. 66, 1125 (1994).
D. Forster, D. R. Nelson, and M. J. Stephen, Phys. Rev. A 16, 732 (1977).
V. V. Lebedev and V. S. L’vov, Pis’ma Zh. Éksp. Teor. Fiz. 58, 301 (1993) [JETP Lett. 58, 310 (1993].
A. M. Polyakov, Gage Fields and Strings (Udmurtski Univ., Izhevsk, 1999).
L. Frachenbourg and Ph. A. Martin, cond-mat/9905056.
R. Tribe and O. Zaboronski, Comm. Math. Phys. 101, 415 (2000).
V. Yakhot and A. Chekhlov, Phys. Rev. Lett. 77, 3118 (1996).
E. Weinan, K. Khanin, A. Mazel, and Y. Sinai, Phys. Rev. Lett. 78, 1904 (1997).
E. Balkovsky, G. Falkovich, I. Kolokolov, and V. Lebedev, Phys. Rev. Lett. 78, 1452 (1997).
R. P. Feynmann and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
M. V. Feigel’man, Zh. Éksp. Teor. Fiz. 79, 1095 (1980) [Sov. Phys. JETP 52, 555 (1980)].
V. Gurarie and A. Migdal, Phys. Rev. E 54, 4908 (1996).
S. A. Boldyrev, Phys. Rev. E 55, 6907 (1997).
T. Gotoh and R. H. Kraichnan, Phys. Fluids 10, 2859 (1998).
J. Bec and U. Frisch, Phys. Rev. E 61, 1395 (2000).
A. I. Chernykh and M. G. Stepanov, Phys. Rev. E 64, 026306 (2001).
G. Falkovich, I. Kolokolov, V. Lebedev, and A. Migdal, Phys. Rev. E 54, 4896 (1996).
M. Chertkov, Phys. Rev. E 55, 2722 (1997).
E. Balkovsky and V. Lebedev, Phys. Rev. E 58, 5776 (1998).
M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, Phys. Rev. E 52, 4924 (1995).
K. Gawedzki and A. Kupianen, Phys. Rev. Lett. 75, 3834 (1995).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 121, No. 6, 2002, pp. 1390–1398.
Original Russian Text Copyright © 2002 by Kolokolov, Turitsyn.
Rights and permissions
About this article
Cite this article
Kolokolov, I.V., Turitsyn, K.S. Dynamic correlations in a thermalized system described by the Burgers equation. J. Exp. Theor. Phys. 94, 1193–1200 (2002). https://doi.org/10.1134/1.1493173
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1493173