Abstract
Based on a solution of the Navier-Stokes equations for the inertial range of fully developed turbulence, a statistical theory is developed to determine the Lagrangian structure functions K n (τ). Over times τ shorter than the large-scale correlation time τc, they obey scaling relations of the form K n (τ) ∞ \( \tau ^{\zeta _n } \). Analytical expressions are derived for ζ n . A detailed comparison between the theory and the experimental results presented in [1] demonstrates complete quantitative agreement. A new concept is introduced in turbulence theory: the correlation R n (τ) between tracer-particle positions on a Lagrangian trajectory. It is shown that the position correlation functions R n exhibit universal scaling behavior for n > 3.
Similar content being viewed by others
References
H. Xu, M. Bourgoin, N. T. Ouellette, and E. Bodenschatz, Phys. Rev. Lett. 96, 024503 (2006).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Butterworth-Heinemann, Oxford, 1987).
U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1996; FAZIS, Moscow, 1998).
K. P. Zybin, V. A. Sirota, A. S. Il’in, and A. V. Gurevich, Zh. Éksp. Teor. Fiz. 132(2), 510 (2007) [JETP 105 (2), 455 (2007)].
G. A. Voth, A. La Porta, A. M. Grawford, et al., arXiv:physics/0110027v2.
P. K. Yeung, Annu. Rev. Fluid Mech. 34, 115 (2002).
C. Beck, Phys. Rev. Lett. 98, 064502 (2007).
R. Benzi, S. Ciliberto, R. Tripiccione, et al., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 48, R29 (1993).
M. E. Artyushkova and D. D. Sokolov, Astron. Zh. 49(7), 584 (2005) [Astron. Rep. 49 (7), 520 (2005)].
L. Biferale, E. Bodenschatz, M. Cencini, et al., arXiv:0708.0311.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.P. Zybin, V.A. Sirota, A.S. Il’in, A.V. Gurevich, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 5, pp. 1024–1033.
Rights and permissions
About this article
Cite this article
Zybin, K.P., Sirota, V.A., Il’in, A.S. et al. Lagrangian structure functions in hydrodynamic turbulence. J. Exp. Theor. Phys. 107, 879–886 (2008). https://doi.org/10.1134/S1063776108110198
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776108110198