Abstract.
Intermittency, measured as \(\log \left({F(r)}/{3}\right)\), where F(r) is the flatness of velocity increments at scale r, is found to rapidly increase as viscous effects intensify, and eventually saturate at very small scales. This feature defines a finite intermediate range of scales between the inertial and dissipation ranges, that we shall call near-dissipation range. It is argued that intermittency is multiplied by a universal factor, independent of the Reynolds number Re, throughout the near-dissipation range. The (logarithmic) extension of the near-dissipation range varies as \(\sqrt{\log Re}\). As a consequence, scaling properties of velocity increments in the near-dissipation range strongly depend on the Reynolds number.
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References
A. Vincent, M. Meneguzzi, J. Fluid Mech. 225, 1 (1991)
Z.-S. She, E. Jackson, S. A. Orszag, Proc. R. Soc. London A 434, 101 (1991)
U. Frisch, R. Morf, Phys. Rev. A 23, 2673 (1981)
O. Chanal, B. Chabaud, B. Castaing, B. Hébral, Eur. Phys. J. B 17, 301 (2000)
J.-F. Pinton, R. Labbé, J. Phys. II France 4, 1461 (1994)
E. Leveque, C. Koudella, Phys. Rev. Lett. 86, 4033 (2001)
N. Cao, S. Chen, Z.-S. She, Phys. Rev. Lett. 76, 3711 (1996)
G. Ruiz-Chavarria, C. Baudet, S. Ciliberto, Phys. Rev. Lett. 74, 1986 (1995)
U. Frisch, Turbulence: the legacy of Kolmogorov, (Cambridge University Press, England, 1995)
B. Castaing, Y. Gagne, M. Marchand, Physica D 68, 387 (1993)
D. Lohse, Phys. Rev. Lett. 73 (24), 3223 (1994)
R.H. Kraichnan, Phys. Fluids 10, 2080 (1967)
G. Paladin, A. Vulpiani, Phys. Rev. A 35, 1971 (1987)
U. Frisch, M. Vergassola, Europhys. Lett. 14, 439 (1991)
M. Nelkin, Phys. Rev. A 42, 7226 (1990)
C. Meneveau, Phys. Rev. E 54, 3657 (1996)
B. Castaing, Y. Gagne, E. Hopfinger, Physica D 46, 177 (1990)
P.-O. Amblard, J.-M. Brossier, Eur. Phys. J. B 12, 579 (1999)
A. Arneodo, S. Manneville, J.-F. Muzy, Eur. Phys. J. B 1, 129 (1998)
J. Delour, J.-F. Muzy, A. Arneodo, Eur. Phys. J. B 23, 243 (2001)
L. Chevillard, Ph.D. thesis, Bordeaux I University (2004), available online at http://tel.ccsd.cnrs.fr
A.N. Kolmogorov, C. R. Acad. Sci. USSR 30, 301 (1941)
V. Emsellem, L.P. Kadanoff, D. Lohse, P. Tabeling, Z.J. Wang, Phys. Rev. E 55, 2672 (1997)
Y. Saito, Phys. Soc. Jpn 61, 403 (1992)
E.A. Novikov, Phys. Rev. E 50, 3303 (1994)
L. Chevillard, S.G. Roux, E. Leveque, N. Mordant, J.-F. Pinton, A. Arneodo, Phys. Rev. Lett. 91, 214502 (2003)
R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Phys. Rev. E 48, R29 (1993)
P.K. Yeung, Y. Zhou, Phys. Rev. E 56, 1746 (1997)
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Chevillard, L., Castaing, B. & Lévêque, E. On the rapid increase of intermittency in the near-dissipation range of fully developed turbulence. Eur. Phys. J. B 45, 561–567 (2005). https://doi.org/10.1140/epjb/e2005-00214-4
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DOI: https://doi.org/10.1140/epjb/e2005-00214-4