Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near<i>d</i>= 4

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.

doi:10.1051/epjconf/201716407044

Cited by 17 publications

(55 citation statements)

References 39 publications

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“…Detailed discussion of this issue and the two-loop calculations in various renormalization schemes can be found in [52]. Similar situation, when a model is logarithmic for arbitrary d but additional UV divergences arise at some exceptional values of d, and extension of the model by adding local terms is required, was encountered recently in [53,54]. Therefore, there are four coupling constants in the full model (2.2) -(2.7):…”

Section: The Kpz Model and The Ns Equationmentioning

confidence: 74%

“…It also would be interesting to study the feedback of the KPZ scalar field on the dynamics of the advecting velocity ("active scalar"). The RG study of this problem for the linear advection-diffusion equation shows that the active term in the NS equation appears IR irrelevant for the turbulent case [56] and for the case thermal equilibrium [57]. One can hope that inclusion of the KPZ nonlinearity will produce a fully nontrivial scaling behaviour where the velocity dynamics is affected by the scalar field.…”

Section: Discussionmentioning

confidence: 99%

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Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation

Antonov,

Gulitskiy,

Kakin

et al. 2020

Preprint

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The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent motion is described by the stochastic Navier-Stokes equation with the random stirring force whose correlation function includes two terms that allow one to account both for a turbulent fluid and for a fluid in thermal equilibrium. The renormalization group analysis performed in the leading order of perturbation theory (one-loop approximation) reveals six possible types of scaling behaviour (universality classes). The most interesting values of the spatial dimension d = 2 and 3 correspond to the universality class of a pure turbulent advection where the nonlinearity of the Kardar-Parisi-Zhang model is irrelevant.

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Section: The Kpz Model and The Ns Equationmentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation

Antonov,

Gulitskiy,

Kakin

et al. 2020

Preprint

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“…Employing dimensional regularization within minimal subtraction scheme (MS) [17] the renormalization constants can be calculated and the UV divergences manifests themselves in pole terms in y and ε = 4 − d. In higher loops pole terms in form of general linear combination in ay + bε may appear.…”

Section: Feynman Diagrammatic Techniquementioning

confidence: 99%

Renormalization group analysis of a turbulent compressible fluid neard= 4: Crossover between local and non-local scaling regimes

et al. 2016

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Abstract. We study scaling properties of the model of fully developed turbulence for a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group (RG). The scaling properties in this approach are related to fixed points of the RG equation. Here we study a possible existence of other scaling regimes and an opportunity of a crossover between them. This may take place in some other space dimensions, particularly at d = 4. A new regime may there arise and then by continuity moves into d = 3. Our calculations have shown that there really exists an additional fixed point, that may govern scaling behaviour.

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“…This paper is a continuation of our previous works [42][43][44][45] and is organized as follows. In the introductory Section 2 we give a brief overview of the model.…”

Section: Introductionmentioning

confidence: 98%

Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4

et al. 2019

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The renormalization group approach and the operator product expansion technique are applied to the model of a passively advected vector field by a turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered in the vicinity of space dimension d = 4 and the perturbation theory is constructed within a double expansion scheme in y and ε = 4 − d , where y describes scaling behaviour of the random force that enters the Navier-Stokes equation. The properties of the correlation functions are investigated, and anomalous scaling and multifractal behaviour are established. All calculations are performed in the leading order of y, ε expansion (one-loop approximation).

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

Cited by 17 publications

References 39 publications

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation

Renormalization group analysis of a turbulent compressible fluid neard= 4: Crossover between local and non-local scaling regimes

Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4

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