Long-Time Tails and the Large-Eddy Behavior of a Randomly Stirred Fluid

Forster, Dieter; Nelson, David R.; Stephen, Michael J.

doi:10.1103/physrevlett.36.867

Cited by 173 publications

(171 citation statements)

References 17 publications

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“…A model with this term only has been analyzed earlier in Ref. [10]. In the theory of turbulence D 20 = 0 should be considered the "real value" of this parameter, since only the first term in Eq.…”

Section: Construction Of the (ε ∆) Expansion In The Two-charge Mmentioning

confidence: 99%

“…Then d = 2 + 2∆ = 2 − 2ε and energy injection (3) becomes local: d f ∼ p 4−d−2ε = p 2 (such a model was considered in Ref. [10]). In this case the multiplicative renormalization (27) conforms to the requirement of local counterterms and the corresponding constants Z do not contain any dependence on log s in accordance with the general theory.…”

Section: Renormalization Of the Model In A Fixed Space Dimension mentioning

confidence: 99%

“…In Ref. [18] (see also [13,14,17]) relation (91) without the extra factor F (ε) was regarded as the definition of the quantity D 10 . Other approaches to the definition of the function C K (ε) and its ε expansion [19] - [25] may be reduced to the introduction of a particular function F (ε) with F (2) = 1 on the right-hand side of relation (91).…”

Section: Skewness Factor and Kolmogorov Constantmentioning

confidence: 99%

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Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

et al. 2005

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An improved ε expansion in the d-dimensional (d > 2) stochastic theory of turbulence is constructed at two-loop order which incorporates the effect of pole singularities at d → 2 in coefficients of the ε expansion of universal quantities. For a proper account of the effect of these singularities two different approaches to the renormalization of the powerlike correlation function of the random force are analyzed near two dimensions. By direct calculation it is shown that the approach based on the mere renormalization of the nonlocal correlation function leads to contradictions at two-loop order. On the other hand, a two-loop calculation in the renormalization scheme with the addition to the force correlation function of a local term to be renormalized instead of the nonlocal one yields consistent results in accordance with the UV renormalization theory. The latter renormalization prescription is used for the two-loop renormalization-group analysis amended with partial resummation of the pole singularities near two dimensions leading to a significant improvement of the agreement with experimental results for the Kolmogorov constant.

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Section: Construction Of the (ε ∆) Expansion In The Two-charge Mmentioning

confidence: 99%

Section: Renormalization Of the Model In A Fixed Space Dimension mentioning

confidence: 99%

Section: Skewness Factor and Kolmogorov Constantmentioning

confidence: 99%

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Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

et al. 2005

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“…This analysis provided a heuristic picture of the damped transient pattern formation. As a continuation of previous work on the continuum limit of a spin representation of a solid-on-solid model for a growing interface [4], we applied in paper II [5] the Martin-Siggia-Rose formalism [6] in its path integral formulation [7,8,9] to the noisy Burgers equation [10,11] and discussed in the weak noise limit the growth morphology and scaling properties in terms of nonlinear soliton excitations with superimposed linear diffusive modes. In paper III [12] we pursued a canonical phase space approach based on the weak noise saddle point approximation to the Martin-Siggia-Rose functional or, alternatively, the Freidlin-Wentzel symplectic approach to the Fokker-Planck equation [13,14].…”

Section: Introductionmentioning

confidence: 99%

Correlations, soliton modes, and non-Hermitian linear mode transmutation in the one-dimensional noisy Burgers equation

Fogedby

2003

Phys. Rev. E

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Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multi-soliton sector, and in detail the correlations and scaling properties in the two-soliton sector.

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“…This equation has the form (Forster et al (1976), Forster et al (1977)) ∂u ∂t = ν∇ 2 u + λu∇u + ∇η ,…”

Section: Introductionmentioning

confidence: 99%

Aspects of the noisy burgers equation

Fogedby¹

Anomalous Diffusion From Basics to Applications

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Abstract. The noisy Burgers equation describing for example the growth of an interface subject to noise is one of the simplest model governing an intrinsically nonequilibrium problem. In one dimension this equation is analyzed by means of the MartinSiggia-Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The growth morphology is characterized by a dilute gas of nonlinear soliton modes with gapless dispersion law E ∝ p 3/2 and a superposed gas of diffusive modes with a gap. The scaling exponents and a heuristic expression for the scaling function follow from a spectral representation.

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Long-Time Tails and the Large-Eddy Behavior of a Randomly Stirred Fluid

Cited by 173 publications

References 17 publications

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

Correlations, soliton modes, and non-Hermitian linear mode transmutation in the one-dimensional noisy Burgers equation

Aspects of the noisy burgers equation

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