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Dynamic multiscaling in turbulence. (English) Zbl 1189.76328

Summary: We give an overview of the progress that has been made in recent years in understanding dynamic multiscaling in homogeneous, isotropic turbulence and related problems. We emphasise the similarity of this problem with the dynamic scaling of time-dependent correlation functions in the vicinity of a critical point in, e.g., a spin system. The universality of dynamic-multiscaling exponents in fluid turbulence is explored by detailed simulations of the GOY shell model for fluid turbulence.

MSC:

76F99 Turbulence

References:

[1] U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University, Cambridge, England, 1996) · Zbl 0844.13014
[2] P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, Cambridge, England, 2004)
[3] V.S. L’vov, E. Podivilov, I. Procaccia, Phys. Rev. E 55, 7030 (1997) · doi:10.1103/PhysRevE.55.7030
[4] D. Mitra, R. Pandit, Phys. Rev. Lett. 93, 2 (2004) · doi:10.1103/PhysRevLett.93.024501
[5] D. Mitra, R. Pandit, Phys. Rev. Lett. 95, 144501 (2005) · doi:10.1103/PhysRevLett.95.144501
[6] V.I. Belinicher, V.S. L’vov, Sov. Phys. JETP 66, 303 (1987)
[7] Y. Kaneda, T. Ishihara, K. Gotoh, Phys. Fluids 11, 2154 (1999) · Zbl 1147.76427 · doi:10.1063/1.870077
[8] F. Hayot, C. Jayaprakash, Phys. Rev. E 57, R4867 (1998) · doi:10.1103/PhysRevE.57.R4867
[9] F. Hayot, C. Jayaprakash, Int. J. Mod. Phys. B 14, 1781 (2000) · doi:10.1142/S0217979200001667
[10] E. Gledzer, Sov. Phys. Dokl. 18, 216 (1973)
[11] K. Ohkitani, M. Yamada, Prog. Theor. Phys. 81, 329 (1989) · doi:10.1143/PTP.81.329
[12] P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (2004) and references therein · doi:10.1103/RevModPhys.49.435
[13] A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 301 (1941)
[14] A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941)
[15] E. Leveque, Z.S. She, Phys. Rev. Lett 75, 2690 (1995) · doi:10.1103/PhysRevLett.75.2690
[16] N. Schorghofer, L. Kadanoff, D. Lohse, Physica D 88, 40 (1995) · Zbl 0899.76244 · doi:10.1016/0167-2789(95)00186-8
[17] P. Ditlevsen, Phys. Fluids 9, 1482 (1997) · Zbl 1185.76751 · doi:10.1063/1.869270
[18] V. Borue, S.A. Orzsag, Phys. Rev. E 51, R856 (1995) · doi:10.1103/PhysRevE.51.R856
[19] V.S. L’vov, I. Procaccia, D. Vandembroucq, Phys. Rev. Lett 81, 802 (1998) · doi:10.1103/PhysRevLett.81.802
[20] V.S. L’vov, R.A. Pasmanter, A. Pomyalov, and I. Procaccia, Phys. Rev. E 67, 066310 (2003) · doi:10.1103/PhysRevE.67.066310
[21] S.B. Pope, Turbulent Flows (Cambridge University, Cambridge, England, 2000)
[22] V.S. L’vov, V.L. Lebedev, Phys. Rev. E 47, 1794 (1993) · doi:10.1103/PhysRevE.47.1794
[23] S.S. Ray, D. Mitra, R. Pandit, to be published
[24] S.K. Dhar, A. Sain, R. Pandit, Phys. Rev. Lett. 78, 2964 (1997) · doi:10.1103/PhysRevLett.78.2964
[25] D. Pisarenko, L. Biferale, D. Courvoisier, U. Frisch, M. Vergassola, Phys. Fluids A 5, 2533 (1993) · Zbl 0799.76032 · doi:10.1063/1.858766
[26] G. Sahoo, D. Mitra, R. Pandit, to be published
[27] L. Kadanoff, D. Lohse, J. Wang, R. Benzi, Phys. Fluids 7, 617 (1995) · Zbl 1039.76508 · doi:10.1063/1.868775
[28] R. Kraichnan, Phys. Fluids 11, 945 (1968) · Zbl 0164.28904 · doi:10.1063/1.1692063
[29] G. Falkovich, K. Gawedzki, M. Vergassola, Rev. Mod. Phys. 73, 913 (2001) · Zbl 1205.76133 · doi:10.1103/RevModPhys.73.913
[30] A. La Porta, G.A. Voth, A.M. Crawford, J. Alexander, E. Bodenschatz, Nature 409, 1017 (2001) · doi:10.1038/35059027
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