Abstract
A self-consistent version of the stochastic theory of turbulence is proposed. The random side force in the Navier-Stokes equation is considered as a dynamic variable controlled by a nonlinear equation of the Ginzburg-Landau type with white noise (equations on this type are used in descriptions of threshold processes). Feedback is provided by the dependence of the symmetry-breaking term in the Ginzburg-Landau equation on the Reynolds number, which is defined as a functional of the velocity field.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Verma, arXiv: nlin. CD/0510069, 2005.
A. N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (PIYaF, St. Petersburg, 1998; Chapman, Boca Raton, 2004).
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, New York, 1975).
S. Samko, A. Kilbas, and O. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Nauka i Tekhnika, Minsk, 1987; Gordon and Breach, London, 1993).
V. E. Tarasov and G. M. Zaslavsky, Physica A 354, 249 (2005).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).
D. N. Zubarev, V. G. Morozov, and O. V. Troshkin, Teor. Mat. Fiz. 92, 293 (1992).
R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 18, 2239 (1985).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.A. Ktitorov, 2007, published in Pis’ma v Zhurnal Tekhnicheskoĭ Fiziki, 2007, Vol. 33, No. 16, pp. 54–58.