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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 469654, 11 pages
The Extended Symmetry Lie Algebra and the Asymptotic Expansion of the Transversal Correlation Function for the Isotropic Turbulence
1Institute of Computational Technologies, Russian Academy of Science, Lavrentjev Avenue 6, Novosibirsk 630090, Russia
2Institute of Mathematics and Statistics, University of Sao Paulo, Rua do Matao 1010, 66281 Sao Paulo, SP, Brazil
3Technical University Darmstadt, Department of Mechanical Engineering, Petersenstrasse 30, 64287 Darmstadt, Germany
Received 4 January 2013; Accepted 12 February 2013
Academic Editor: Rutwig Campoamor-Stursberg
Copyright © 2013 V. N. Grebenev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. N. Grebenev and M. Oberlack, “Geometric realization of the two-point velocity correlation tensor for isotropic turbulence,” Journal of Nonlinear Mathematical Physics, vol. 18, no. 1, pp. 109–120, 2011.
- V. N. Grebenev, M. Oberlack, and A. N. Grishkov, “Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence,” Zeitschrift für angewandte Mathematik und Physik.
- V. N. Grebenev and M. Oberlack, “A geometry of the correlation space and a nonlocal degenerate parabolic equation from isotropic turbulence,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 92, no. 3, pp. 179–195, 2012.
- Th. von Kármán and L. Howarth, “On the statistical theory of isotropic turbulence,” Proceedings of the Royal Society A, vol. 164, pp. 192–215, 1938.
- G. Falkovich, “Conformal invariance in hydrodynamic turbulence,” Russian Mathematical Surveys, vol. 62, no. 3, pp. 497–510, 2007.
- D. Bernard, G. Bofffeta, A. Celani, and G. Falkovich, “Conformal invariance in two-dimensional turbulence,” Nature Physics, vol. 2, pp. 124–128, 2006.
- J. Cardy, “The power of two dimensions,” Nature Physics, vol. 2, pp. 67–68, 2006.
- S. Oughton, K.-H. Rädler, and W. H. Matthaeus, “General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence,” Physical Review E, vol. 56, no. 3, pp. 2875–2888, 1997.
- A. S. Monin and A. M. Yaglom, Statistical Hydromechanics, Gidrometeoizdat, St. Petersburg, Russia, 1994.
- J. C. Rotta, Turbulente Strömungen, Teubner, Stuttgar, Russia, 1972.
- N. R. Kamyshanskij and A. S. Solodovnikov, “Semireducible analytic spaces “in the large”,” Russian Mathematical Surveys, vol. 35, no. 5, pp. 1–56, 1980.
- L. P. Eisenhart, Riemannian Geometry, Princeton University Press, Princeton, NJ, USA, 1926.
- A. G. Megrabov, “Group spliting and Lax representation,” Doklady Mathematics, vol. 67, no. 3, pp. 335–349, 2003.
- S. V. Meleshko, “Homogeneous autonomous systems with three independent variables,” Journal of Applied Mathematics and Mechanics, vol. 58, no. 5, pp. 857–863, 1994.
- A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory,” Nuclear Physics B, vol. 241, no. 2, pp. 333–380, 1984.
- M. Schottenloher, A Mathematical Introduction to Conformal Field Theory, vol. 759 of Lecture Notes in Physics, Springer, Berlin, Germany, 2nd edition, 2008.