N. V. Antonov

Renormalization group, operator product expansion, and anomalous scaling in a model of advected passive scalar

A statistical model of strongly anisotropic fully developed turbulence of the weakly compressible fluid is considered by means of the field theoretic renormalization group. The corrections due to compressibility to the infrared form of the kinetic energy spectrum have been calculated in the leading order in the Mach number expansion. Furthermore, in this approximation the validity of the Kolmogorov hypothesis on the independence of the dissipation length of velocity correlation functions in the inertial range has been proved.

RENORMALIZATION-GROUP APPROACH TO THE STOCHASTIC NAVIER–STOKES EQUATION: TWO-LOOP APPROXIMATION

The field theoretic renormalization group is applied to the stochastic Navier--Stokes equation that describes fully developed fluid turbulence. The complete two-loop calculation of the renormalization constant, the

Renormalization group in the infinite-dimensional turbulence: third-order results

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Renormalization group in turbulence theory: Exactly solvable Heisenberg model

function, the fixed point and the ultraviolet correction exponent is performed. The Kolmogorov constant and the inertial-range skewness factor, derived to second order of the

Renormalization group in the problem of fully developed turbulence of a compressible fluid

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Composite operators, operator expansion, and Galilean invariance in the theory of fully developed turbulence. Infrared corrections to Kolmogorov scaling

expansion, are in a good agreement with the experiment. The possibility of the extrapolation of the

Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields

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Random interface growth in a random environment: Renormalization group analysis of a simple model

expansion beyond the threshold where the sweeping effects become important is demonstrated on the example of a Galilean-invariant quantity, the equal-time pair correlation function of the velocity field. The extension to the

Anomalous scaling in statistical models of passively advected vector fields

d

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling.

-dimensional case is briefly discussed.