Abstract.
Intermittency is a basic feature of fully developed turbulence, for both velocity and passive scalars. Intermittency is classically characterized by Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework to characterize the temporal intermittency of the velocity and passive scalar concentration of a an element of fluid advected by a turbulent intermittent field. Here we focus on Lagrangian passive scalar scaling exponents, and discuss their possible links with Eulerian passive scalar and mixed velocity-passive scalar structure functions. We provide different transformations between these scaling exponents, associated to different transformations linking space and time scales. We obtain four new explicit relations. Experimental data are needed to test these predictions for Lagrangian passive scalar scaling exponents.
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References
Z. Warhaft, Annual Rev. Fluid Mech. 32, 203 (2000)
S. Pope, Turbulent flows (Cambridge University Press, 2000)
A.N. Kolmogorov, C. R. Acad. Sci. URSS 30, 301 (1941)
A.M. Obukhov, Izv. Akad. Nauk. SSSR Geogr. Geofiz. 13, 58 (1949)
S. Corrsin, J. Appl. Phys. 22, 469 (1951)
H. Tennekes, J.L. Lumley, A First Course in Turbulence (MIT Press, 1972)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (MIR, 1944), first russian edition
E. Inoue, J. Meteorol. Soc. Jpn. 29, 246 (1952)
U. Frisch, Turbulence; the legacy of A. N. Kolmogorov (Cambridge University Press, 1995)
L'héritage de Kolmogorov en physique, edited by R. Livi, A. Vulpiani (Belin, Paris, 2003)
T. Bohr, M.H. Jensen, G. Paladin, A. Vulpiani, Dynamical systems approach to turbulence (Cambridge University Press, 1998)
D. Schertzer, S. Lovejoy, F. Schmitt, Y. Chigirinskaya, D. Marsan, Fractals 5, 427 (1997)
A. Arnéodo, C. Baudet, F. Belin, R. Benzi, B. Castaing, B. Chabaud, R. Chavarria, S. Ciliberto, R. Camussi, F. Chilla, et al. Europhys. Lett. 34, 411 (1996)
R.H. Kraichnan, Phys. Rev. Lett. 72, 1016 (1994)
G. Falkovich, K. Gawedzki, M. Vergassola, Rev. Mod. Phys. 73, 913 (2001)
R.A. Antonia, E.J. Hopfinger, Y. Gagne, F. Anselmet, Phys. Rev. A 30, 2704 (1984)
G. Ruiz-Chavarria, C. Baudet, S. Ciliberto, Physica D 99, 369 (1996)
F.G. Schmitt, D. Schertzer, S. Lovejoy, Y. Brunet, Europhys. Lett. 34, 195 (1996)
O.N. Boratav, R.B. Pelz, Phys. Fluids 10, 2122 (1998)
G. Xu, R.A. Antonia, S. Rajagopalan, Europhys. Lett. 49, 452 (2000)
F. Moisy, H. Willaime, J.S. Andersen, P. Tabeling, Phys. Rev. Lett. 86, 4827 (2001)
A. Gylfason, Z. Warhaft, Phys. Fluids 16, 4012 (2004)
T. Watanabe, T. Gotoh, New J. Phys. 6, 40 (2004)
R.A. Antonia, C.W.V. Atta, J. Fluid Mech. 67, 273 (1975)
C. Meneveau, K.R. Sreenivasan, P. Kailasnath, M.S. Fan, Phys. Rev. A 41, 894 (1990)
L. Seuront, F.G. Schmitt, Deep Sea Res. II 52, 1308 (2005)
A.M. Yaglom, Dokl. Akad. Nauk. SSSR 69, 743 (1949)
J.-F. Pinton, F. Plaza, L. Danaila, P.L. Gal, F. Anselmet, Physica D 122, 187 (1998)
E. Lévêque, G. Ruiz-Chavarria, C. Baudet, S. Ciliberto, Phys. Fluids 11, 1869 (1999)
R. Rao, Phys. Rev. E 59, 1727 (1999)
L. Mydlarski, J. Fluid Mech. 475, 173 (2003)
E.A. Novikov, Phys. Fluids A 1, 326 (1989)
L. Seuront, F. Schmitt, D. Schertzer, Y. Lagadeuc, S. Lovejoy, Nonlinear Proc. Geophys. 3, 236 (1996)
L. Seuront, F.G. Schmitt, Geophys. Res. Lett. 31, L03306 (2004)
F.G. Schmitt, Physica A (submitted)
M.S. Borgas, Phil. Trans. R. Soc. Lond. A 342, 379 (1993)
N. Mordant, O. Michel, P. Metz, J.-F. Pinton, Phys. Rev. Lett. 87, 21 (2001)
L. Chevillard, S.G. Roux, E. Lévêque, N. Mordant, J.-F. Pinton, A. Arnéodo, Phys. Rev. Lett. 91, 214502 (2003)
L. Chevillard, (Ph.D. thesis, University of Bordeaux I available online at http://tel.ccsd.cnrs.fr (2004)
G. Boffetta, F.D. Lillo, S. Musacchio, Phys. Rev. E 66, 066307 (2002)
L. Biferale, G. Boffetta, A. Celani, B.J. Devenish, A. Lanotte, F. Toschi, Phys. Rev. Lett. 93, 064502 (2004)
L. Biferale, G. Boffetta, A. Celani, A. Lanotte, F. Toschi, Phys. Fluids 17, 021701 (2005)
L.F. Richardson, Proc. Roy. Soc. London A 110, 709 (1926)
G. Parisi, U. Frisch, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by M. Ghil, R. Benzi, G. Parisi (North Holland, Amsterdam, 1985), 84
F.G. Schmitt, Phys. Lett. A 342, 448 (2005)
Y.G. Sinai, V. Yakhot, Phys. Rev. Lett. 63, 1962 (1989)
S. Vaienti, M. Ould-Rouis, F. Anselmet, P.L. Gal, Physica D 73, 99 (1994)
D. Schertzer, S. Lovejoy, J. Geophys. Res. 92, 9692 (1987)
B.W. Zeff, D.L. Lanterman, R. McAllister, R. Roy, E.J. Kostelich, D.P. Lathrop, Nature 421, 146 (2003)
M. Chertkov, A. Pumir, B.I. Shraiman, Phys. Fluids 11, 2394 (1999)
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Schmitt, F. Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence. Eur. Phys. J. B 48, 129–137 (2005). https://doi.org/10.1140/epjb/e2005-00374-1
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DOI: https://doi.org/10.1140/epjb/e2005-00374-1