An improved $\eps$ expansion for three-dimensional turbulence: summation of nearest dimensional singularities

Abstract

An improved $\eps$ expansion in the $d$-dimensional ($d>2$) stochastic theory of turbulence is constructed by taking into account pole singularities at $d\to 2$ in coefficients of the $\eps$ expansion of universal quantities. Effectiveness of the method is illustrated by a two-loop calculation of the Kolmogorov constant in three dimensions.

arXiv comment4 pages

References in corpus (1)

• Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation

Cited by in corpus (6)

• Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
• An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
• Two-loop calculation of the turbulent Prandtl number
• Turbulent compressible fluid: renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields
• Renormalization group analysis of a turbulent compressible fluid near $d=4$ : Crossover between local and non-local scaling regimes
• Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation