Two-parameter expansion in the renormalization-group analysis of turbulence

Honkonen, Juha; Nalimov, M. Yu.

doi:10.1007/bf02769945

Cited by 18 publications

(61 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Ref. [5] a different scheme of renormalization was adopted based on the general statement of the theory of UV renormalization that the counterterms are local. In the one-loop approximation, to which the authors of Refs.…”

Section: Introductionmentioning

confidence: 99%

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

et al. 2005

Self Cite

View full text Add to dashboard Cite

An improved ε expansion in the d-dimensional (d > 2) stochastic theory of turbulence is constructed at two-loop order which incorporates the effect of pole singularities at d → 2 in coefficients of the ε expansion of universal quantities. For a proper account of the effect of these singularities two different approaches to the renormalization of the powerlike correlation function of the random force are analyzed near two dimensions. By direct calculation it is shown that the approach based on the mere renormalization of the nonlocal correlation function leads to contradictions at two-loop order. On the other hand, a two-loop calculation in the renormalization scheme with the addition to the force correlation function of a local term to be renormalized instead of the nonlocal one yields consistent results in accordance with the UV renormalization theory. The latter renormalization prescription is used for the two-loop renormalization-group analysis amended with partial resummation of the pole singularities near two dimensions leading to a significant improvement of the agreement with experimental results for the Kolmogorov constant.

show abstract

Section: Introductionmentioning

confidence: 99%

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

et al. 2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that parameters ǫ = 2, a = 1 are the natural "physical" values in our "massless" power-law energy injection. The introduction of the local correlations (proportional to the new couplings g v20 , and g b20 ) which are described by the analytic in k 2 terms in the correlation functions (3), and (4) is related to the existence of additional divergences of this structure (see below in the text) in the two dimensional model which cannot be removed by corresponding nonlocal terms [24,32,33]. At the same time, the localness of the counterterms is the fundamental feature of a model to be multiplicatively renormalizable [34,13].…”

Section: Functional Formulation Of Double Expansion Modelmentioning

confidence: 99%

“…The expression of the β(g(s)) function is known in the framework of the δ, ǫ expansion (see (24) and also (18)). The fixed point g * (s → 0) satisfies a system of equations β g (g * ) = 0, while a IR stable fixed point, weakly dependent on initial conditions, is defined by positive definiteness of the real part of the matrix Ω = (∂β g /∂g)| g * (the matrix of the first derivatives taken at the fixed point).…”

Section: Rg Equationsmentioning

confidence: 99%

“…On the other hand, it was also supposed that in two dimensions the magnetic fixed point does not exist as a result of nonexistence of the IR stable magnetic fixed point. But the conclusions about two dimensional fixed points cannot be consider without doubts in these papers due to the problems with renormalization in two dimensions which were not taken into account [24] (see also [5]). In [25,26] two dimensional case was studied too but again with shortcomings, therefore their results cannot be considered completely conclusive.…”

Section: Introductionmentioning

confidence: 97%

“…It was accomplished within a two-parameter expansion (double expansion) of scaling exponents and scaling functions [24] where, besides the parameter which characterize the deviation of the exponent of the powerlike correlation function of random forcing from its critical value, the additional parameter of the deviation of the spatial dimension was introduced. The using of this double expansion method has allowed them to confirm the basic conclusions of the previous works [10,17], namely, the nonexistence of the magnetic scaling regime near two dimensions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

D-dimensional developed MHD turbulence: double expansion model

Jurčišin¹,

Stehlík²

2006

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Abstract. Developed magnetohydrodynamic turbulence near two dimensions d up to three dimensions has been investigated by means of renormalization group approach and double expansion regularization. A modification of standard minimal subtraction scheme has been used to analyze the stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. The exact analytical expressions have been obtained for the fixed points. The continuation of the universal value of the inverse Prandtl number u = 1.562 determined at d = 2 up to d = 3 restores the value of u = 1.393 which is known in the kinetic fixed point from usual ǫ-expansion. The magnetic stable fixed point has been calculated and its stability region has been also examined. This point losses stability: (1) below critical value of dimension dc = 2.36 (independently on the a-parameter of a magnetic forcing) and, (2) below the value of ac = 0.146 (independently on the dimension).

show abstract

Stochastic Navier-Stokes Equation for a Compressible Fluid: Two-Loop Approximation

Hnatič

Gulitskiy

Lučivjanský

et al. 2019

11th Chaotic Modeling and Simulation International Conference

View full text Add to dashboard Cite

A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be obtained and further analyzed by means of the perturbative renormalization group. Two fixed points of the RG equations are found. The perturbation theory is constructed within formal expansion scheme in parameter y, which describes scaling behavior of random force fluctuations. Actual calculations for fixed points' coordinates are performed to two-loop order.

show abstract

Two-parameter expansion in the renormalization-group analysis of turbulence

Cited by 18 publications

References 10 publications

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

D-dimensional developed MHD turbulence: double expansion model

Stochastic Navier-Stokes Equation for a Compressible Fluid: Two-Loop Approximation

Contact Info

Product

Resources

About