Renormalization-Group Approach to the Stochastic Navier–stokes Equation: Two-Loop Approximation

Adzhemyan, L. Ts.; Antonov, N. V.; Kompaniets, M. V.; Васильев, А. Н.

doi:10.1142/s0217979203018193

Cited by 59 publications

(46 citation statements)

References 27 publications

(57 reference statements)

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“…Unfortunately, the interesting physical case, obtained for y = 4 and corresponding to the Kolmogorov spectrum for the velocity field, lies in a range where convergence of the RG expansion is not granted [25]. Notwithstanding extensions of the RG formalism to y ∼ O(1), values which have been attempted by different approaches [23,24], the problem is still open. Recent numerical simulations tried to shed light on this issue [26,27] but, because of the limited resolution, their results are not conclusive.…”

Section: Introductionmentioning

confidence: 99%

Anomalous scaling and universality in hydrodynamic systems with power-law forcing

et al. 2004

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The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study passive scalars advected by a 2d velocity field in the inverse cascade regime. For the nonlinear case, we review a recent investigation of 3d Navier-Stokes turbulence, and we present new quantitative results for shell models of turbulence. We show that to get firm statements is necessary to reach considerably high resolutions due to the presence of unavoidable subleading terms affecting all correlation functions. All findings support universality of anomalous scaling for the small scale fluctuations.

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Section: Introductionmentioning

confidence: 99%

Anomalous scaling and universality in hydrodynamic systems with power-law forcing

et al. 2004

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“…Размерный анализ действия (7) для пространственной размерности d > 2 [8], [11] показывает, что модель является логарифмической при ε = 0, т. е. постоянная вза-имодействия g 0 в этой точке безразмерна, и что наивные УФ-расходимости имеют вид полюсов по ε и представлены только в одночастично-неприводимых функциях ⟨v…”

Section: ренормгрупповой анализunclassified

“…Здесь коэффициенты z В случае отсутствия спиральности (ρ = 0) разложение постоянных перенорми-ровки Z i , i = 1, 2, известно с точностью до второго порядка по g (двухпетлевое приближение) [8], [9], [11]. Простейший однопетлевой результат для z…”

Section: ренормгрупповой анализunclassified

Нарушение Пространственной Четности И Турбулентное Магнитное Число Прандтля

Юрчишинова¹,

Jurčišinová²,

Юрчишин³

et al. 2013

ТМФ

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НАРУШЕНИЕ ПРОСТРАНСТВЕННОЙ ЧЕТНОСТИ И ТУРБУЛЕНТНОЕ МАГНИТНОЕ ЧИСЛО ПРАНДТЛЯС использованием теоретико-полевых ренормгрупповых методов в двухпет-левом приближении исследуется влияние спиральности (нарушения простран-ственной четности) на турбулентное магнитное число Прандтля в модели кине-матической магнитoгидродинамической турбулентности, когда магнитное поле ведет себя как пассивная векторная величина, переносимая средой со спираль-ной турбулентностью, задаваемой стохастическим уравнением Навье-Стокса. Показано, что наличие спиральности уменьшает значение турбулентного маг-нитного числа Прандтля и что двухпетлевой спиральный вклад в турбулентное магнитное число Прандтля достигает 4.2% от его значения в отсутствие спи-ральности. Этот результат демонстрирует сильную устойчивость свойств диф-фузионных процессов в магнитном поле в турбулентных средах с нарушением пространственной четности по сравнению с соответствующими системами без спиральности.Ключевые слова: развитая турбулентность, пассивный перенос, спиральность, ренор-мализационная группа.

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“…The problem has also been eased by an intricate analysis of the large-scale stirring (sweeping), using "short-distance operator-product expansions" in the RNG analysis, and accounting for Galilean invariance (see, e.g., Ref. [17]). …”

Section: Modern Mathematical Fluid Mechanics Began In 1755 Withmentioning

confidence: 99%

Turbulence: Large-scale sweeping and the emergence of small-scale Kolmogorov spectra

Dekker

2011

Phys. Rev. E

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Link to publication Citation for published version (APA):Dekker, H. (2011). Turbulence: Large-scale sweeping and the emergence of small-scale Kolmogorov spectra. Physical Review E, 84(2), [026302]. DOI: 10.1103/PhysRevE.84.026302 General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. The dynamics of fully developed hydrodynamic turbulence still is a basically unsolved theoretical problem, due to the strong-coupling long-range nonlinearities in the Navier-Stokes equations. The present analysis focuses on the small-scale fluctuations in a turbulent boundary layer with one external length scale y o . After taking a (2+1)D spatiotemporal spectral transform of the fluctuating vorticity fields, care is taken of large-scale sweeping which arises as a collective zero mode from the nonlinear flow terms. The "unswept" small-scale nonlinearities are then shown to be asymptotically locally isotropic (i.e., for wave numbers k→∞) by internal consistency, which allows to close the nonlinear hierarchy. The Navier-Stokes equations (without external forcing) are integrated to give the spectral response of the fluctuating small-scale velocity fields on the presence of a locally isotropic blob of turbulence while it is being swept around over an arbitrary steady state mean velocity profile, using viscous boundary conditions at y=0. Averaging the response spectrum over all possible orientational configurations and sweep velocities results in a novel self-consistency integral for the 4D energy spectrum function. The distribution of turbulence sweep velocities is modeled by means of Lévy-type densities, having an algebraic tail with power p > 1. The generic case (which includes Von Kármán's logarithmic mean velocity profile) is found to correspond to 1 < p < 3. Asymptotic analysis of the self-consistency integral leads to a differential equation which fixes the scaling exponent λ of the unswept frequency and admits a nonempty, integrable and positive definite Airy-type frequency spectrum E ı (k, /k λ ) ∼ k μ with so-called "normal" Kolmogorov scaling, that is, μ = −7/3 and λ = 2/3. Anomalous scaling is possible for one special mean profile.

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Renormalization-Group Approach to the Stochastic Navier–stokes Equation: Two-Loop Approximation

Cited by 59 publications

References 27 publications

Anomalous scaling and universality in hydrodynamic systems with power-law forcing

Anomalous scaling and universality in hydrodynamic systems with power-law forcing

Нарушение Пространственной Четности И Турбулентное Магнитное Число Прандтля

Turbulence: Large-scale sweeping and the emergence of small-scale Kolmogorov spectra

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