Stochastic Navier–Stokes Equation with Colored Noise: Renormalization Group Analysis

• Main Authors: Antonov N. V., Gulitskiy N. M., Malyshev A. V.
• Format: Article
• Language: English
• Published: EDP Sciences 2016-01-01
• Series: EPJ Web of Conferences
• Online Access: http://dx.doi.org/10.1051/epjconf/201612604019

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.