arXiv subjects

Yu. S. Kabrits

Publications and source records attributed to Yu. S. Kabrits.

3 recordsLinked to original sources

arXiv2002

Two-loop calculation of the scaling behavior of two-dimensional forced Navier-Stokes equation

Asymptotic properties of the solution of two-dimensional randomly forced Navier-Stokes equation with long-range correlations of the driving force are analyzed in the two-loop order of perturbation theory with the use of renormalization group. Kolmogorov constant of the energy spectrum is calculated for both the inverse energy cascade and the direct enstrophy cascade in the second order of the $ε$ expansion.

nlin.CD↗

arXiv2001

Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order $\varepsilon^{3}$

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function $\proptoδ(t-t')/k^{d+\eps}$. Inertial-range anomalous exponents, identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients, are calculated within the $\varepsilon$ expansion to order $\varepsilon^{3}$ (three-loop approximation), including the exponents in anisotropic sectors. The main goal of the paper is to give the complete derivation of this third-order result, and to present and explain in detail the corresponding calculational techniques. The character and convergence properties of the $\varepsilon$ expansion are discussed; the improved ``inverse'' $\varepsilon$ expansion is proposed and the comparison with the existing nonperturbative results is given.

nlin.CD↗

arXiv2001

Anomalous exponents in the rapid-change model of the passive scalar advection in the order $ε^{3}$

Field theoretic renormalization group is applied to the Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - <{\bf v}(t,{\bf x}){\bf v}(t',{\bf x'})> \proptoδ(t-t')|{\bf x}-{\bf x'} |^ε$. Inertial-range anomalous exponents, related to the scaling dimensions of tensor composite operators built of the scalar gradients, are calculated to the order $ε^{3}$ of the $ε$ expansion. The nature and the convergence of the $ε$ expansion in the models of turbulence is are briefly discussed.

nlin.CD↗