Correlation functions in isotropic and anisotropic turbulence: The role of the symmetry group

Arad, Itai; L’vov, Victor S.; Procaccia, Itamar

doi:10.1103/physreve.59.6753

Cited by 128 publications

(219 citation statements)

References 12 publications

Supporting

Mentioning

213

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Turbulence with pressure: Anomalous scaling of a passive vector field

et al. 2003

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Turbulence with pressure: Anomalous scaling of a passive vector field

et al. 2003

View full text Add to dashboard Cite

show abstract

“…Here Φ ℓm (r) = r ℓ Y ℓm (r), and see [1] for further details. The first two spherical vectors have a different parity than the third vector, hence the equations for their coefficients are decoupled from the equation for the third coefficient.…”

Section: B the So(3) Decompositionmentioning

confidence: 99%

“…A simple calculation [1] shows that these belong to a twodimensional subspace, which is spanned by the "incompressible vectors"…”

Section: B the So(3) Decompositionmentioning

confidence: 99%

See 1 more Smart Citation

Spectrum of anisotropic exponents in hydrodynamic systems with pressure

Arad

Procaccia

2001

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We discuss the scaling exponents characterizing the power-law behavior of the anisotropic components of correlation functions in turbulent systems with pressure. The anisotropic components are conveniently labeled by the angular momentum index ℓ of the irreducible representation of the SO(3) symmetry group. Such exponents govern the rate of decay of anisotropy with decreasing scales. It is a fundamental question whether they ever increase as ℓ increases, or they are bounded from above. The equations of motion in systems with pressure contain nonlocal integrals over all space. One could argue that the requirement of convergence of these integrals bounds the exponents from above. It is shown here on the basis of a solvable model (the "linear pressure model"), that this is not necessarily the case. The model introduced here is of a passive vector advection by a rapidly varying velocity field. The advected vector field is divergent free and the equation contains a pressure term that maintains this condition. The zero modes of the second-order correlation function are found in all the sectors of the symmetry group. We show that the spectrum of scaling exponents can increase with ℓ without bounds, while preserving finite integrals. The conclusion is that contributions from higher and higher anisotropic sectors can disappear faster and faster upon decreasing the scales also in systems with pressure.

show abstract

Lagrangian Description of Turbulence

Falkovich

Gawędzki

Vergassola

Les Houches - Ecole D’Ete De Physique Theorique

View full text Add to dashboard Cite

Correlation functions in isotropic and anisotropic turbulence: The role of the symmetry group

Cited by 128 publications

References 12 publications

Turbulence with pressure: Anomalous scaling of a passive vector field

Turbulence with pressure: Anomalous scaling of a passive vector field

Spectrum of anisotropic exponents in hydrodynamic systems with pressure

Lagrangian Description of Turbulence

Contact Info

Product

Resources

About