Comptes Rendus
Structures and statistics of fluid turbulence / Structures et statistiques de la turbulence des fluides
Insight on turbulent flows from Lagrangian tetrads
[Un éclairage sur les écoulements turbulents par lʼétude de tétrades lagrangiennes]
Comptes Rendus. Physique, Volume 13 (2012) no. 9-10, pp. 889-898.

La connaissance trop partielle des mécanismes de génération des petites échelles dans les écoulements turbulents est une sérieuse entrave à la compréhension et à la prédiction quantitative de nombreux problèmes physiques, appliqués ou fondamentaux, et nécessite donc dʼutiliser de nouvelles approches. Nous passons en revue les informations qui peuvent être obtenues en suivant le mouvement de quelques traceurs dans un écoulement turbulent. Cette approche, qui a montré son efficacité dans lʼétude de la dispersion dʼun scalaire passif transporté par la turbulence, a conduit à un éclairage nouveau sur quelques-uns des phénomènes surprenants observés dans des écoulements turbulents, tels que lʼalignement de la vorticité avec les vecteurs propres du tenseur de taux de déformation. De récents travaux ont porté sur le mouvement de quatre particules formant initialement une tétrade régulière de taille r0. Les perspectives de modélisation inspirées par cette approche sont présentées et discutées.

The insufficient understanding of the generation of small scales in turbulent flows results in serious impediment when trying to describe numerous physical problems, of natural or applied significance, and therefore, calls for new approaches. Here, we discuss the insight that can be gained by following the motion of a few points in a turbulent flow. This approach, which has shown its power in the context of the problem of dispersion of a passive scalar transported by turbulence, has led to new insight into some of the intriguing phenomena observed in turbulent flows, such as the alignment of vorticity with the eigenvectors of the rate of strain tensor. Recent work has focused on the motion of four points, forming initially a regular tetrad of size r0. In particular, the modeling perspective inspired by the tetrad approach will be discussed here.

Publié le :
DOI : 10.1016/j.crhy.2012.09.001
Keywords: Turbulence, Flow structure, Scale dependence, Modeling
Mot clés : Turbulence, Structure de lʼécoulement, Dépendance dʼéchelle, Modélisation

Alain Pumir 1 ; Aurore Naso 2

1 Laboratoire de physique, Ecole normale supérieure de Lyon, CNRS and université de Lyon 1, 46, allée dʼItalie, 69007 Lyon, France
2 Laboratoire de mécanique des fluides et dʼacoustique, Ecole centrale de Lyon, CNRS and université Lyon 1, 36, avenue Guy-de-Collongue, 69134 Ecully, France
@article{CRPHYS_2012__13_9-10_889_0,
     author = {Alain Pumir and Aurore Naso},
     title = {Insight on turbulent flows from {Lagrangian} tetrads},
     journal = {Comptes Rendus. Physique},
     pages = {889--898},
     publisher = {Elsevier},
     volume = {13},
     number = {9-10},
     year = {2012},
     doi = {10.1016/j.crhy.2012.09.001},
     language = {en},
}
TY  - JOUR
AU  - Alain Pumir
AU  - Aurore Naso
TI  - Insight on turbulent flows from Lagrangian tetrads
JO  - Comptes Rendus. Physique
PY  - 2012
SP  - 889
EP  - 898
VL  - 13
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crhy.2012.09.001
LA  - en
ID  - CRPHYS_2012__13_9-10_889_0
ER  - 
%0 Journal Article
%A Alain Pumir
%A Aurore Naso
%T Insight on turbulent flows from Lagrangian tetrads
%J Comptes Rendus. Physique
%D 2012
%P 889-898
%V 13
%N 9-10
%I Elsevier
%R 10.1016/j.crhy.2012.09.001
%G en
%F CRPHYS_2012__13_9-10_889_0
Alain Pumir; Aurore Naso. Insight on turbulent flows from Lagrangian tetrads. Comptes Rendus. Physique, Volume 13 (2012) no. 9-10, pp. 889-898. doi : 10.1016/j.crhy.2012.09.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2012.09.001/

[1] A.N. Kolmogorov Dokl. Akad. Nauk SSSR, 30 (1941), p. 301

[2] G.I. Barenblatt; Ya.B. Zeldovich Self-similar solutions as intermediate asymptotics, Ann. Rev. Fluid Mech., Volume 4 (1972), p. 295

[3] F. Anselmet; Y. Gagne; E.J. Hopfinger; R.A. Antonia High-order velocity structure functions in turbulent shear flows, J. Fluid Mech., Volume 140 (1984), p. 63

[4] Z.S. She; E. Leveque Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., Volume 72 (1994), p. 336

[5] U. Frisch Turbulence, Cambridge University Press, 1996

[6] G. Falkovich; I. Fouxon; Y. Oz New relations for correlation functions in Navier–Stokes turbulence, J. Fluid Mech., Volume 644 (2010), p. 465

[7] R. Friedrich; A. Daitche; O. Kamps; J. Lülff; M. Voßkuhle; M. Wilczek The Lundgren–Monin–Novikov hierarchy: kinetic equations for turbulence, C. R. Phys., Volume 13 (2012), pp. 929-953

[8] A. Pumir; E.D. Siggia Collapsing solutions to the 3-D Euler equations, Phys. Fluids A, Volume 2 (1990), p. 220

[9] R.M. Kerr Evidence for a singularity of the three-dimensional incompressible Euler equations, Phys. Fluids A, Volume 5 (1993), p. 1725

[10] T. Grafke; H. Homann; J. Dreher; R. Grauer Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods, Physica D, Volume 237 (2008), p. 14

[11] S.S. Girimaji; S.B. Pope A diffusion model for velocity gradients in turbulence, Phys. Fluids A, Volume 2 (1990), p. 242

[12] J. Martin; C. Dopazo; L. Valino Dynamics of velocity gradient invariants in turbulence: restricted Euler and linear diffusion models, Phys. Fluids, Volume 10 (1998), p. 2012

[13] E. Jeong; S.S. Girimaji Velocity-gradient dynamics in turbulence: effect of viscosity and forcing, Theoret. Comput. Fluid Dyn., Volume 16 (2003), p. 421

[14] Y. Li; C. Meneveau Origin of non-Gaussian statistics in hydrodynamic turbulence, Phys. Rev. Lett., Volume 95 (2005), p. 164502

[15] L. Chevillard; C. Meneveau Lagrangian dynamics and statistical geometric structure of turbulence, Phys. Rev. Lett., Volume 97 (2006), p. 174501

[16] C. Meneveau Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows, Ann. Rev. Fluid Mech., Volume 43 (2011), p. 219

[17] F. van der Bos; B. Tao; C. Meneveau; J. Katz Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements, Phys. Fluids, Volume 14 (2002), p. 2457

[18] B.W. Zeff; D.D. Lanterman; R. McAllister; R. Roy; E.J. Kostelich; D.P. Lathrop Measuring intense rotation and dissipation in turbulent flows, Nature, Volume 421 (2003), p. 146

[19] L. Mydlarski; A. Pumir; B. Shraiman; E.D. Siggia; Z. Warhaft Structures and multipoint correlators for turbulent advection: predictions and experiments, Phys. Rev. Lett., Volume 81 (2008), p. 4373

[20] B.I. Shraiman; E.D. Siggia Scalar turbulence, Nature, Volume 405 (2000), p. 639

[21] Z. Warhaft Passive scalars in turbulent flows, Ann. Rev. Fluid Mech., Volume 32 (2000), p. 203

[22] M. Chertkov; A. Pumir; B.I. Shraiman Lagrangian tetrad dynamics and the phenomenology of turbulence, Phys. Fluids, Volume 11 (1999), p. 2394

[23] R.H. Kraichnan Convection of a passive scalar by a quasi uniform random straining field, J. Fluid Mech., Volume 64 (1974), p. 737

[24] B.I. Shraiman; E.D. Siggia Anomalous scaling of a passive scalar in turbulent flow, C. R. Acad. Sci. Ser. II, Paris, Volume 321 (1995), p. 279

[25] G. Falkovich; K. Gawedzki; M. Vergassola Particles and fields in fluid turbulence, Rev. Mod. Phys., Volume 73 (2001), p. 913 (is that the Lagrangian point of view)

[26] W.H. Press; S.A. Teukolsky; W.T. Vetterling; B.P. Flannery Numerical Recipes in Fortran 77, Cambridge University Press, 1992

[27] B.J. Cantwell On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence, Phys. Fluids A, Volume 5 (1993), p. 2008

[28] A. Pumir; B.I. Shraiman; M. Chertkov Geometry of Lagrangian dispersion in turbulence, Phys. Rev. Lett., Volume 85 (2000), p. 5324

[29] L. Biferale; G. Boffetta; A. Celani; B.J. Devenish; A. Lanotte; F. Toschi Multiparticle dispersion in fully developed turbulence, Phys. Fluids, Volume 17 (2005), p. 111701

[30] H. Xu; N.T. Ouellette; E. Bodenschatz Evolution of geometric structures in intense turbulence, New J. Phys., Volume 10 (2008), p. 013012

[31] J.F. Hackl; P.K. Yeung; B.L. Sawford Multi-particle and tetrad statistics in numerical simulations of turbulent relative dispersion, Phys. Fluids, Volume 23 (2011), p. 065103

[32] E.D. Siggia Invariants for the one-point vorticity and strain rate correlation functions, Phys. Fluids (1981), p. 1934

[33] K.K. Nomura; G.K. Post The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence, J. Fluid Mech., Volume 377 (1998), p. 65

[34] M. Guala; B. Luthi; A. Liberzon; A. Tsinober; W. Kinzelbach On the evolution of material lines and vorticity in homogeneous turbulence, J. Fluid Mech., Volume 533 (2005), p. 339

[35] Wm.T. Ashurst; A.R. Kerstein; R.M. Kerr; C.H. Gibson Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence, Phys. Fluids (1987), p. 2343

[36] Z.S. She; E. Jackson; S.A. Orszag Structure and dynamics of homogeneous turbulence. Models and simulations, Proc. R. Soc. Lond. A, Volume 434 (1991), p. 101

[37] A. Tsinober; E. Kit; T. Dracos Experimental investigation of the field of velocity gradients in turbulent flows, J. Fluid Mech., Volume 242 (1992), p. 169

[38] H. Xu; A. Pumir; E. Bodenschatz The Pirouette effect in turbulent flows, Nat. Phys., Volume 7 (2011), p. 709

[39] L. Chevillard; C. Meneveau Lagrangian time correlations of vorticity alignments in isotropic turbulence: observations and model predictions, Phys. Fluids, Volume 23 (2011), p. 101704

[40] A. Pumir, E. Bodenschatz, H. Xu, Tetrahedron deformation and alignment of perceived velocity and strain in a turbulent flow, Phys. Fluids (2012), submitted for publication, . | arXiv

[41] H. Tennekes; J.L. Lumley A First Course in Turbulence, MIT Press, Cambridge, 1972

[42] A. Naso; A. Pumir Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence, Phys. Rev. E, Volume 72 (2005), p. 056318

[43] A. Naso; A. Pumir; M. Chertkov Statistical geometry in homogeneous and isotropic turbulence, J. Turbul., Volume 8 (2007), p. 39

[44] A. Pumir; A. Naso Statistical properties of the coarse-grained velocity gradient tensor in turbulence: Monte Carlo simulations of the tetrad model, New J. Phys., Volume 12 (2010), p. 123024

[45] P. Grassberger Pruned-enriched Rosenbluth method: simulation of θ-polymers of chain length up to 1000000, Phys. Rev. E, Volume 56 (1997), p. 3682

[46] D.A. Adams; L.M. Sander; R.M. Ziff The barrier method: a technique for calculating very long transition times, J. Chem. Phys., Volume 41 (2010), p. 8

Cité par Sources :

Commentaires - Politique