[Un éclairage sur les écoulements turbulents par lʼétude de tétrades lagrangiennes]
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 . 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 . In particular, the modeling perspective inspired by the tetrad approach will be discussed here.
Mot clés : Turbulence, Structure de lʼécoulement, Dépendance dʼéchelle, Modélisation
@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},
}
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] Dokl. Akad. Nauk SSSR, 30 (1941), p. 301
[2] Self-similar solutions as intermediate asymptotics, Ann. Rev. Fluid Mech., Volume 4 (1972), p. 295
[3] High-order velocity structure functions in turbulent shear flows, J. Fluid Mech., Volume 140 (1984), p. 63
[4] Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., Volume 72 (1994), p. 336
[5] Turbulence, Cambridge University Press, 1996
[6] New relations for correlation functions in Navier–Stokes turbulence, J. Fluid Mech., Volume 644 (2010), p. 465
[7] The Lundgren–Monin–Novikov hierarchy: kinetic equations for turbulence, C. R. Phys., Volume 13 (2012), pp. 929-953
[8] Collapsing solutions to the 3-D Euler equations, Phys. Fluids A, Volume 2 (1990), p. 220
[9] Evidence for a singularity of the three-dimensional incompressible Euler equations, Phys. Fluids A, Volume 5 (1993), p. 1725
[10] Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods, Physica D, Volume 237 (2008), p. 14
[11] A diffusion model for velocity gradients in turbulence, Phys. Fluids A, Volume 2 (1990), p. 242
[12] Dynamics of velocity gradient invariants in turbulence: restricted Euler and linear diffusion models, Phys. Fluids, Volume 10 (1998), p. 2012
[13] Velocity-gradient dynamics in turbulence: effect of viscosity and forcing, Theoret. Comput. Fluid Dyn., Volume 16 (2003), p. 421
[14] Origin of non-Gaussian statistics in hydrodynamic turbulence, Phys. Rev. Lett., Volume 95 (2005), p. 164502
[15] Lagrangian dynamics and statistical geometric structure of turbulence, Phys. Rev. Lett., Volume 97 (2006), p. 174501
[16] Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows, Ann. Rev. Fluid Mech., Volume 43 (2011), p. 219
[17] 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] Measuring intense rotation and dissipation in turbulent flows, Nature, Volume 421 (2003), p. 146
[19] Structures and multipoint correlators for turbulent advection: predictions and experiments, Phys. Rev. Lett., Volume 81 (2008), p. 4373
[20] Scalar turbulence, Nature, Volume 405 (2000), p. 639
[21] Passive scalars in turbulent flows, Ann. Rev. Fluid Mech., Volume 32 (2000), p. 203
[22] Lagrangian tetrad dynamics and the phenomenology of turbulence, Phys. Fluids, Volume 11 (1999), p. 2394
[23] Convection of a passive scalar by a quasi uniform random straining field, J. Fluid Mech., Volume 64 (1974), p. 737
[24] Anomalous scaling of a passive scalar in turbulent flow, C. R. Acad. Sci. Ser. II, Paris, Volume 321 (1995), p. 279
[25] Particles and fields in fluid turbulence, Rev. Mod. Phys., Volume 73 (2001), p. 913 (is that the Lagrangian point of view)
[26] Numerical Recipes in Fortran 77, Cambridge University Press, 1992
[27] On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence, Phys. Fluids A, Volume 5 (1993), p. 2008
[28] Geometry of Lagrangian dispersion in turbulence, Phys. Rev. Lett., Volume 85 (2000), p. 5324
[29] Multiparticle dispersion in fully developed turbulence, Phys. Fluids, Volume 17 (2005), p. 111701
[30] Evolution of geometric structures in intense turbulence, New J. Phys., Volume 10 (2008), p. 013012
[31] Multi-particle and tetrad statistics in numerical simulations of turbulent relative dispersion, Phys. Fluids, Volume 23 (2011), p. 065103
[32] Invariants for the one-point vorticity and strain rate correlation functions, Phys. Fluids (1981), p. 1934
[33] The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence, J. Fluid Mech., Volume 377 (1998), p. 65
[34] On the evolution of material lines and vorticity in homogeneous turbulence, J. Fluid Mech., Volume 533 (2005), p. 339
[35] Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence, Phys. Fluids (1987), p. 2343
[36] Structure and dynamics of homogeneous turbulence. Models and simulations, Proc. R. Soc. Lond. A, Volume 434 (1991), p. 101
[37] Experimental investigation of the field of velocity gradients in turbulent flows, J. Fluid Mech., Volume 242 (1992), p. 169
[38] The Pirouette effect in turbulent flows, Nat. Phys., Volume 7 (2011), p. 709
[39] 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] A First Course in Turbulence, MIT Press, Cambridge, 1972
[42] Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence, Phys. Rev. E, Volume 72 (2005), p. 056318
[43] Statistical geometry in homogeneous and isotropic turbulence, J. Turbul., Volume 8 (2007), p. 39
[44] 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] Pruned-enriched Rosenbluth method: simulation of θ-polymers of chain length up to , Phys. Rev. E, Volume 56 (1997), p. 3682
[46] The barrier method: a technique for calculating very long transition times, J. Chem. Phys., Volume 41 (2010), p. 8
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