Asymptotic behavior of the solution of the two-dimensional stochastic vorticity equation

Honkonen, Juha

doi:10.1103/physreve.58.4532

Cited by 14 publications

(42 citation statements)

References 22 publications

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“…as predicted by perturbative renormalization [17,23]. Note that negative values of λ 1 are admissible if the overall "force" vertex remains positive definite.…”

Section: Approximated Renormalization Group Flowmentioning

confidence: 99%

“…However, the situation completely differs in two dimensions [21,22]. On the one hand, perturbative renormalization group analysis [23] upholds the validity of (4) for any ε. On the other hand, the asymptotic solution of the Kármán-Howarth-Monin equation [22] shows that (4) is always subdominant with respect to the inverse energy cascade spectrum E(p) ∝ p −5/3 , for ε 2, i.e., even in the regime where renormalization group analysis should apply.…”

Section: Introductionmentioning

confidence: 99%

“…The Legendre antitransform of (26) reconstruct the convex envelope of the free energy (23). In this sense, the average action may be interpreted as an ultraviolet regularization of the theory.…”

Section: A Thermodynamic Formalismmentioning

confidence: 99%

“…Locality entitles us to interpret this term as a renormalization counterterm in the sense of Refs. [23,37,38]. Again, we will use the extra freedom introduced by F m r to impose a renormalization condition on the flow.…”

Section: B Flow Equationsmentioning

confidence: 99%

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Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Mejía‐Monasterio

Muratore-Ginanneschi

2012

Phys. Rev. E

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We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4 − 2 ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

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“…as predicted by perturbative renormalization [17,23]. Note that negative values of λ 1 are admissible if the overall "force" vertex remains positive definite.…”

Section: Approximated Renormalization Group Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: A Thermodynamic Formalismmentioning

confidence: 99%

Section: B Flow Equationsmentioning

confidence: 99%

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Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Mejía‐Monasterio

Muratore-Ginanneschi

2012

Phys. Rev. E

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“…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%

D-dimensional developed MHD turbulence: double expansion model

Jurčišin¹,

Stehlík²

2006

J. Phys. A: Math. Gen.

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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).

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Breaking of Scale Invariance in Correlation Functions of Turbulence

Tarpin

2020

Springer Theses

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Asymptotic behavior of the solution of the two-dimensional stochastic vorticity equation

Cited by 14 publications

References 22 publications

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

D-dimensional developed MHD turbulence: double expansion model

Breaking of Scale Invariance in Correlation Functions of Turbulence

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