Anomalous and dimensional scaling in anisotropic turbulence

Biferale, L.; Boffetta, G.; Celani, A.; Lanotte, A.; Toschi, F.; Vergassola, M. Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. We present the results of a numerical investigation of three-dimensional decaying turbulence with statistically homogeneous and anisotropic initial conditions. We show that at large times, in the inertial range of scales: ͑i͒ isotropic velocity fluctuations decay self-similarly at an algebraic rate which can be obtained by dimensional arguments; ͑ii͒ the ratio of anisotropic to isotropic fluctuations of a given intensity falls off in time as a power law, with an exponent approximately independent of the strength of the fluctuation; ͑iii͒ the decay of anisotropic fluctuations is not self-similar, their statistics becoming more and more intermittent as time elapses. We also investigate the early stages of the decay. The different short-time behavior observed in two experiments differing by the phase organization of their initial conditions gives a new hunch on the degree of universality of small-scale turbulence statistics, i.e., its independence of the conditions at large scales.

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“…In analogy with the observations made in the stationary case 18,[20][21][22][23][24][25][26] we postulate a scaling behavior…”

Section: ͑6͒supporting

confidence: 77%

The decay of homogeneous anisotropic turbulence

et al. 2003

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“…It was shown that the leading terms of the inertial-range behavior are the same for isotropic and anisotropic forcing [57,58]. In the papers [59][60][61][62], the velocity correlation functions were decomposed in the irreducible representations of the rotation group. It was argued that in each sector of the decomposition, scaling behavior can be found with apparently universal exponents.…”

Section: Discussionmentioning

confidence: 99%

“…The picture outlined above for passively advected fields (a superposition of power laws with universal exponents and nonuniversal amplitudes) seems rather general, being compatible with that established recently in the field of NS turbulence, on the basis of numerical simulations of channel flows and experiments in the atmospheric surface layer; see Refs. [57][58][59][60][61][62] and references therein. It was shown that the leading terms of the inertial-range behavior are the same for isotropic and anisotropic forcing [57,58].…”

Section: Discussionmentioning

confidence: 99%

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Turbulence with pressure: Anomalous scaling of a passive vector field

et al. 2003

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The field theoretic renormalization group (RG) and the operator product expansion are applied to the model of a transverse (divergence-free) vector quantity, passively advected by the "synthetic" turbulent flow with a finite (and not small) correlation time. The vector field is described by the stochastic advection-diffusion equation with the most general form of the inertial nonlinearity; it contains as special cases the kinematic dynamo model, linearized Navier-Stokes (NS) equation, the special model without the stretching term that possesses additional symmetries and has a close formal resemblance with the stochastic NS equation. The statistics of the advecting velocity field is Gaussian, with the energy spectrum E(k) ∝ k 1−ε and the dispersion law ω ∝ k −2+η , k being the momentum (wave number). The inertial-range behavior of the model is described by seven regimes (or universality classes) that correspond to nontrivial fixed points of the RG equations and exhibit anomalous scaling. The corresponding anomalous exponents are associated with the critical dimensions of tensor composite operators built solely of the passive vector field, which allows one to construct a regular perturbation expansion in ε and η; the actual calculation is performed to the first order (one-loop approximation), including the anisotropic sectors. Universality of the exponents, their (in)dependence on the forcing, effects of the large-scale anisotropy, compressibility and pressure are discussed. In particular, for all the scaling regimes the exponents obey a hierarchy related to the degree of anisotropy: the more anisotropic is the contribution of a composite operator to a correlation function, the faster it decays in the inertial-range. The relevance of these results for the real developed turbulence described by the stochastic NS equation is discussed.

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“…Since the two forcing functions studied here are both to some degree anisotropic and inhomogeneous, subleading contributions due to departures from full symmetry could be responsible for this discrepancy. In this context, a decomposition of the structure functions into their isotropic and anisotropic components [18,53,54] could help to asses the degree of universality of each component. These points will necessitate further study and better resolved flows.…”

Section: Effects Of Different Forcing Functions a Forcing Expressmentioning

confidence: 99%

Large-scale flow effects, energy transfer, and self-similarity on turbulence

2006

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The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256 3 to 1024 3 , are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity is also investigated. We discuss the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect. Finally, we briefly describe the consequences of our results for the subgrid modeling of turbulent flows.

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Anomalous and dimensional scaling in anisotropic turbulence

Cited by 37 publications

References 19 publications

The decay of homogeneous anisotropic turbulence

The decay of homogeneous anisotropic turbulence

Turbulence with pressure: Anomalous scaling of a passive vector field

Large-scale flow effects, energy transfer, and self-similarity on turbulence

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