Turbulent Prandtl number in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>model of passive vector admixture

Jurčišinová, E.; Jurčišin, M.; Remecký, R.

doi:10.1103/physreve.93.033106

Cited by 20 publications

(90 citation statements)

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“…The inequality ∆ (n,0) < ∆ (p,0) + ∆ (k,0) , which follows from both explicit one-loop expressions (26) and (27), indicates, that the operators F (n,0) demonstrate a "multifractal" behavior; see [41].…”

Section: Operator Product Expansionmentioning

confidence: 99%

“…Both expressions (26) and (27) suppose higher order corrections in y and ε. Therefore, the infinite set of operators with negative critical dimensions, whose spectra is unbounded from below, is observed.…”

Section: Tracer Fieldmentioning

confidence: 99%

“…with the dimensions ∆ (2n,0) given by the expressions (26) and (27) with the substitution l = 0. Other types of fields or other numbers of derivatives generate the more "distant" corrections.…”

Section: Operator Product Expansionmentioning

confidence: 99%

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Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization neard= 4

et al. 2017

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Abstract. The renormalization group approach and the operator product expansion technique are applied to the model of a tracer field advected by the Navier-Stokes velocity ensemble for a compressible fluid. The model is considered in the vicinity of the specific space dimension d = 4. The properties of the equal-time structure functions are investigated. The multifractal behaviour of various correlation functions is established. All calculations are performed in the leading one-loop approximation.

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Section: Operator Product Expansionmentioning

confidence: 99%

Section: Tracer Fieldmentioning

confidence: 99%

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Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization neard= 4

et al. 2017

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“…The RG analysis of the field theoretic model described by the action functional (5) is based on analysis of UV divergences of the model. The detailed analysis is given in [15].…”

Section: Mathematical Model Of the Turbulent Systemmentioning

confidence: 99%

Diffusion Processes in the A-Model of Vector Admixture: Turbulent Prandtl Number

2018

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Abstract. Using analytical approach of the field theoretic renormalization-group technique in two-loop approximation we model a fully developed turbulent system with vector characteristics driven by stochastic Navier-Stokes equation. The behaviour of the turbulent Prandtl number Pr A,t is investigated as a function of parameter A and spatial dimension d > 2 for three cases, namely, kinematic MHD turbulence (A = 1), the admixture of a vector impurity by the Navier-Stokes turbulent flow (A = 0) and the model of linearized Navier-Stokes equation (A = −1). It is shown that for A = −1 the turbulent Prandtl number is given already in the one-loop approximation and does not depend on d while turbulent Prandt numbers in first two cases show very similar behaviour as functions of dimension d in the two-loop approximation.

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“…(6.39) gives the desired asymptotic behavior of the scaling functions 40) where the summation runs over all the Galilean invariant scalar operators (including operators with derivatives, etc. ), with the coefficient functions A F analytical in their arguments.…”

Section: E Operator Product Expansion and Anomalous Scalingmentioning

confidence: 99%

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

et al. 2017

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We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed points of the renormalization group equations. Previous analysis of this model near the real-world space dimension 3 identified some scaling regime [Theor. Math. Phys., 110, 3 (1997)]. The aim of the present paper is to explore the existence of additional regimes, that could not be found using the direct perturbative approach of the previous work, and to analyze the crossover between different regimes. It seems possible to determine them near the special value of space dimension 4 in the framework of double y and ε expansion, where y is the exponent associated with the random force and ε = 4 − d is the deviation from the space dimension 4. Our calculations show that there exists an additional fixed point that governs scaling behavior. Turbulent advection of a passive scalar (density) field by this velocity ensemble is considered as well. We demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. The corresponding anomalous exponents, identified as scaling dimensions of certain composite fields, can be systematically calculated as a series in y and ε. All calculations are performed in the leading one-loop approximation.

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Turbulent Prandtl number in theAmodel of passive vector admixture

Cited by 20 publications

References 50 publications

Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization neard= 4

Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization neard= 4

Diffusion Processes in the A-Model of Vector Admixture: Turbulent Prandtl Number

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

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