Abstract
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.
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References
U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University, Cambridge, England, 1996)
P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, Cambridge, England, 2004)
V.S. L’vov, E. Podivilov, I. Procaccia, Phys. Rev. E 55, 7030 (1997)
D. Mitra, R. Pandit, Phys. Rev. Lett. 93, 2 (2004)
D. Mitra, R. Pandit, Phys. Rev. Lett. 95, 144501 (2005)
V.I. Belinicher, V.S. L’vov, Sov. Phys. JETP 66, 303 (1987)
Y. Kaneda, T. Ishihara, K. Gotoh, Phys. Fluids 11, 2154 (1999)
F. Hayot, C. Jayaprakash, Phys. Rev. E 57, R4867 (1998)
F. Hayot, C. Jayaprakash, Int. J. Mod. Phys. B 14, 1781 (2000)
E. Gledzer, Sov. Phys. Dokl. 18, 216 (1973)
K. Ohkitani, M. Yamada, Prog. Theor. Phys. 81, 329 (1989)
P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (2004) and references therein
A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 301 (1941)
A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941)
E. Leveque, Z.S. She, Phys. Rev. Lett 75, 2690 (1995)
N. Schorghofer, L. Kadanoff, D. Lohse, Physica D 88, 40 (1995)
P. Ditlevsen, Phys. Fluids 9, 1482 (1997)
V. Borue, S.A. Orzsag, Phys. Rev. E 51, R856 (1995)
V.S. L’vov, I. Procaccia, D. Vandembroucq, Phys. Rev. Lett 81, 802 (1998)
V.S. L’vov, R.A. Pasmanter, A. Pomyalov, and I. Procaccia, Phys. Rev. E 67, 066310 (2003)
S.B. Pope, Turbulent Flows (Cambridge University, Cambridge, England, 2000)
V.S. L’vov, V.L. Lebedev, Phys. Rev. E 47, 1794 (1993)
S.S. Ray, D. Mitra, R. Pandit, to be published
S.K. Dhar, A. Sain, R. Pandit, Phys. Rev. Lett. 78, 2964 (1997)
D. Pisarenko, L. Biferale, D. Courvoisier, U. Frisch, M. Vergassola, Phys. Fluids A 5, 2533 (1993)
G. Sahoo, D. Mitra, R. Pandit, to be published
L. Kadanoff, D. Lohse, J. Wang, R. Benzi, Phys. Fluids 7, 617 (1995)
R. Kraichnan, Phys. Fluids 11, 945 (1968)
G. Falkovich, K. Gawedzki, M. Vergassola, Rev. Mod. Phys. 73, 913 (2001)
A. La Porta, G.A. Voth, A.M. Crawford, J. Alexander, E. Bodenschatz, Nature 409, 1017 (2001)
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Pandit, R., Ray, S.S. & Mitra, D. Dynamic multiscaling in turbulence. Eur. Phys. J. B 64, 463–469 (2008). https://doi.org/10.1140/epjb/e2008-00048-6
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DOI: https://doi.org/10.1140/epjb/e2008-00048-6