Abstract
Statistical characteristics of a passive scalar advected by a turbulent velocity field are considered in the decay problem with a low scalar diffusivity κ (large Prandtl number v/κ, where v is kinematic viscosity). A regime in which the scalar correlation length remains smaller than the velocity correlation length is analyzed. The equal-time correlation functions of the scalar field are found to vary according to power laws and have angular singularities reflecting locally layered distribution of the scalar in space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, 3rd ed. (Nauka, Moscow, 1986; Pergamon, New York, 1987).
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics, 2nd ed. (Gidrometeoizdat, St. Petersburg, 1996; MIT Press, Cambridge, 1975).
A. N. Kolmogorov, Dokl. Akad. Nauk 32, 16 (1941).
U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge Univ. Press, Cambridge, 1995; Fazis, Moscow, 1998).
R. H. Kraichnan and D. Montgomery, Rep. Prog. Phys. 43, 547 (1980).
R. H. Kraichnan, Phys. Fluids 7, 1723 (1964); Adv. Math. 16, 305 (1975).
G. Falkovich and V. Lebedev, Phys. Rev. E 50, 3883 (1994); 49, 1800 (1994).
G. K. Batchelor, J. Fluid Mech. 5, 113 (1959).
A. Groisman and V. Steinberg, Nature 405, 53 (2000).
R. H. Kraichnan, Phys. Fluids 11, 945 (1968).
A. P. Kazantsev, Zh. Éksp. Teor. Fiz. 53, 1806 (1967) [Sov. Phys. JETP 26, 1031 (1967)].
G. Falkovich, K. Gaw
dzki, and M. Vergassola, Rev. Mod. Phys. 73, 913 (2001).M. Chertkov and V. Lebedev, Phys. Rev. Lett. 90, 034501 (2003).
M. Chaves, G. Eyink, U. Frisch, and M. Vergassola, Phys. Rev. Lett. 86, 2305 (2001).
E. Balkovsky and A. Fouxon, Phys. Rev. E 60, 4164 (1999).
M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, Int. J. Mod. Phys. B 10, 2273 (1996); Phys. Rev. E 51, 5609 (1995).
R. Ellis, Entropy, Large Deviations and Statistical Mechanics (Springer, Berlin, 1985).
S. S. Girimaji and S. B. Pope, J. Fluid Mech. 220, 427 (1990).
I. Goldhirsch, P.-L. Sulem, and S. A. Orszag, Physica D (Amsterdam) 27, 311 (1987).
Y. Amarouchene and H. Kellay, Phys. Rev. Lett. 93, 214504 (2004).
X.-L. Wu, B. Martin, H. Kellay, and W. I. Goldburg, Phys. Rev. Lett. 75, 236 (1994).
G. Falkovich, I. Kolokolov, V. Lebedev, and A. Migdal, Phys. Rev. E 54, 4896 (1996).
I. V. Kolokolov and K. S. Turitsyn, Zh. Éksp. Teor. Fiz. 121, 1219 (2002) [JETP 94, 1193 (2002)]
E. Balkovsky, M. Chertkov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 52, 4924 (1995); Pis’ma Zh. Éksp. Teor. Fiz. 61, 1012 (1995) [JETP Lett. 61, 1049 (1995)].
E. Balkovsky, G. Falkovich, V. Lebedev, and M. Lysiansky, Phys. Fluids 11, 2269 (1999).
M.-C. Jullien, P. Castiglione, and P. Tabeling, Phys. Rev. Lett. 85, 3636 (2000).
A. Gamba and I. V. Kolokolov, J. Stat. Phys. 94, 759 (1999).
dzki, and M. Vergassola, Rev. Mod. Phys. 73, 913 (2001).Author information
Authors and Affiliations
Additional information
Original Russian Text © S.S. Vergeles, 2006, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 129, No. 4, pp. 777–796.
Rights and permissions
About this article
Cite this article
Vergeles, S.S. Spatial dependence of correlation functions in the decay problem for a passive scalar in a large-scale velocity field. J. Exp. Theor. Phys. 102, 685–701 (2006). https://doi.org/10.1134/S1063776106040194
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1063776106040194