Infrared properties of an anisotropically stirred fluid

Rubinstein, Robert; Barton, J. M.

doi:10.1063/1.866077

Cited by 21 publications

(21 citation statements)

References 17 publications

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“…The same argument applies for the present case of passively advected vector field as well. The uniaxial anisotropy projector (13) has already been widely used in analyzes of the anisotropically driven Navier-Stokes equation, MHD turbulence equations and passive advection equations [21]. However, these studies were limited to the investigation of the existence and stability of the fixed points with the subsequent calculation of the critical dimensions of the basic quantities leaving the calculation of the anomalous exponents in those models an open problem.…”

Section: Kinematic Mhd Kazantsev-kraichnan Modelmentioning

confidence: 99%

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

et al. 2005

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Inertial-range scaling behavior of high-order (up to order N = 51) structure functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. It has been shown that in inertial range the leading terms of the structure functions are coordinate independent, but powerlike corrections appear with the same anomalous scaling exponents as for the passively advected scalar field. These exponents depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to structure functions have not been found.

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Section: Kinematic Mhd Kazantsev-kraichnan Modelmentioning

confidence: 99%

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

et al. 2005

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“…The last relation in (30) results from the absence of renormalization of the contribution with D 0 , so that D 0 ≡ g 0 ν 0 = gµ ε ν; see (4). No renormalization of the fields, anisotropy parameters and the "mass" m is required, i.e., Z Φ = 1 for all Φ, and so on.…”

Section: Renormalization Rg Functions and Rg Equationsmentioning

confidence: 99%

“…In a number of papers, e.g., [30][31][32][33][34], the RG techniques were applied to the anisotropically driven Navier-Stokes equation, including passive advection and magnetic turbulence, with the expression (14) entering into the stirring force correlator. The detailed account can be found in Ref.…”

mentioning

confidence: 99%

Anomalous scaling of a passive scalar in the presence of strong anisotropy

Adzhemyan¹,

Antonov²,

Hnatich³

et al. 2000

Phys. Rev. E

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Field theoretic renormalization group and the operator product expansion are applied to a model of a passive scalar quantity θ(t, x), advected by the Gaussian strongly anisotropic velocity field with the covariance ∝ δ(t − t ′ )|x − x ′ | ε . Inertial-range anomalous scaling behavior is established, and explicit asymptotic expressions for the structure functions Sn(r) ≡ [θ(t, x + r) − θ(t, x)] n are obtained; they are represented by superpositions of power laws with nonuniversal (dependent on the anisotropy parameters) anomalous exponents, calculated to the first order in ε in any space dimension d. In the limit of vanishing anisotropy, the exponents are associated with tensor composite operators built of the scalar gradients, and exhibit a kind of hierarchy related to the degree of anisotropy: the less is the rank, the less is the dimension and, consequently, the more important is the contribution to the inertial-range behavior. The leading terms of the even (odd) structure functions are given by the scalar (vector) operators. For the finite anisotropy, the exponents cannot be associated with individual operators (which are essentially "mixed" in renormalization), but the aforementioned hierarchy survives for all the cases studied. The second-order structure function S2 is studied in more detail using the renormalization group and zero-mode techniques; the corresponding exponents and amplitudes are calculated within the perturbation theories in ε, 1/d, and in the anisotropy parameters. If the anisotropy of the velocity is strong enough, the skewness factor S3/S 3/2 2 increases going down towards to the depth of the inertial range; the higher-order odd ratios increase even if the anisotropy is weak.

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“…It means that 2d turbulence is very sensitive to the anisotropy and no stable scaling regimes exist in this case. In the case d = 3, for both the isotropic turbulence and anisotropic one, as it has been mentioned above, existence of the stable fixed point, which governs the Kolmogorov asymptotic regime, has been established by means of the RG approach by using the analytical regularization procedure [6,7,9]. One can make analytical continuation from d = 2 to the three-dimensional turbulence (in the same sense as in the theory of critical phenomena) and verify whether the stability of the fixed point (or, equivalently, stability of the Kolmogorov scaling regime) is restored.…”

Section: Introductionmentioning

confidence: 99%

“…In some cases it has been found out that stability really takes place (see,e.g. [6,7]). On the other hand, existence of systems without such a stability has been proved too.…”

Section: Introductionmentioning

confidence: 99%

Stability of scaling regimes ind>~2developed turbulence with weak anisotropy

et al. 2001

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The fully developed turbulence with weak anisotropy is investigated by means of renormalization group approach (RG) and double expansion regularization for dimensions d ≥ 2. Some modification of the standard minimal substraction scheme has been used to analyze stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. This fixed point is unstable at d = 2; thus, the infinitesimally weak anisotropy destroyes above scaling regime in two-dimensional space. The restoration of the stability of this fixed point, under transition from d = 2 to d = 3, has been demonstrated at borderline dimension 2 < d c < 3. The results are in qualitative agreement with ones obtained recently in the framework of the usual analytical regularization scheme.

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Infrared properties of an anisotropically stirred fluid

Cited by 21 publications

References 17 publications

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Anomalous scaling of a passive scalar in the presence of strong anisotropy

Stability of scaling regimes ind>~2developed turbulence with weak anisotropy

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