Stochastic Navier–Stokes Equation with Colored Noise: Renormalization Group Analysis
1 Department of Theoretical Physics, Faculty of Physics, Saint Petersburg State University, Ulyanovskaja 1, Saint Petersburg–Petrodvorez, 198504 Russia
2 State Scientific Centre “Institute for Theoretical and Experimental Physics” of National Research Centre “Kurchatov Institute”, B. Cheremushkinskaya 25, Moscow, 117218 Russia
Published online: 4 November 2016
In this work we study the fully developed turbulence described by the stochastic Navier–Stokes equation with finite correlation time of random force. Inertial-range asymptotic behavior is studied in one-loop approximation and by means of the field theoretic renormalization group. The inertial-range behavior of the model is described by limiting case of vanishing correlation time that corresponds to the nontrivial fixed point of the RG equation. Another fixed point is a saddle type point, i.e., it is infrared attractive only in one of two possible directions. The existence and stability of fixed points depends on the relation between the exponents in the energy spectrum ε ∝ k1−y and the dispersion law ω ∝ k2−η.
© The Authors, published by EDP Sciences, 2016
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