Multifractal asymptotic modeling of the probability density function of velocity increments in turbulence

Physica D: Nonlinear Phenomena

Volumn 129, Issue 1-2, 1999, Pages 93-114

  Tcheou J M ^a,b   Brachet, M E ^a   Belin, F ^a   Tabeling, P ^a   Willaime, H ^a  

^a CNRS   (France)

^b AXA   (France)

Author keywords

Intermittency; Moments; Multifractal scaling law; Probability density function; Steepest descent method; Turbulence

Indexed keywords

EID: 0346457332     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00307-8     Document Type: Article

References (24)

1. A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds number, C. R. Acad. Sci., USSR 30 (1941) 9-13.
2. A.N. Kolmogorov, On degeneration decay of isotropic turbulence in an incompressible viscous liquid, C. R. Acad. Sci., USSR 31 (1941) 538-540.
3. A.N. Kolmogorov, Dissipation of energy in locally isotropic turbulence, C. R. Acad. Sci., USSR 32 (1941) 16-18.
4. A.N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech. 13 (1962) 82-85.
5. A.M. Obukhov, Some specific features of atmospheric turbulence, J. Fluid Mech. 13 (1962) 77-81 .
6. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, Cambridge, 1995.
7. E.A. Novikov, R.W. Stewart, The intermittency of turbulence and the spectrum of energy dissipation, Izv. Akad. Nauk. SSSR Ser. Geoffiz. 3 (1964) 408-413.
8. U. Frisch, P.L. Sulem, M. Nelkin, A simple dynamical model of intermittent fully developed turbulence, J. Fluid Mech. 87 (1978) 719-736.
9. B.B. Mandelbrot, On intermittent free turbulence, in: Turbulence of Fluids and Plasmas, Brooklyn Polytechnic Institute, 1968.
10. B.B. Mandelbrot, Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, J. Fluid Mech. 62 (1974) 331-358.
11. C.W. Van Atta, W. Y. Chen, Structure functions of the turbulence in the atmospheric boundary layer over the ocean, J. Fluid Mech. 44 (1970) 145-159.
12. F. Anselmet, Y. Gagne, E.J. Hopfinger, R.A. Antonia, High order velocity structure functions in turbulent shear flow, J. Fluid Mech. 140 (1984) 63-89.
13. Y. Gagne, Etude Expérimentale de l'intermittence et des singularités dans le plan complexe en turbulence développée. PhD Thesis, Université de Grenoble, France, 1987.
14. G. Parisi, U. Frisch, On the singularity structure of fully developed turbulence, in: M. Ghil, R. Benzi, G. Parisi (Eds.), Turbulence and Predictability in Geophysical Fluid Dynamics, Proc. Int. School of Physics 'E. Fermi', 1983, Varenna, Italy, North-Holland, Amsterdam, 1985, pp. 84-87.
15. B.B. Mandelbrot, Random multifractal: negative dimensions and the resulting limitations of the thermodynamic formalism, Proc. R. Soc. London, Ser. A 434 (1991) 79-88.
16. P. Kalilasnath, K.R. Sreenivasan, G. Stolovitsky, Probability density of velocity increments in turbulent flows, Phys. Rev. Lett. 68 (1992) 2766-2769.
17. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48 (1993) R29-R32.
18. J.M. Tchéou, Analyse statistique multifractale en turbulence pleinement développée et application à la finance. PhD Thesis, Ecole Normale Supérieure de Cachan, France, 1997.
19. C.M. Bender, S.A. Orszag, Advanced mathematical methods for scientists and engineers, in: International Series in Pure and Applied Mathematics, McGraw-Hill, New York, 1978.
20. J. Maurer, P. Tabeling, G. Zocchi, Statistics of turbulence between two counter-rotating disks in low temperature helium gas, Europhys. Lett. 26 (1994) 31-36.
21. P. Tabeling, G. Zocchi, F. Belin, J. Maurer, H. Willaime, Probability density functions, skewness and flatness in large Reynolds number turbulence, Phys. Rev. E 53 (1996) 1613-1621.
22. F. Belin, P. Tabeling, H. Willaime, Exponents of the structure function in a helium experiment, Physica D 93 (1995) 52-63.
23. J.M. Tchéou, M.E. Brachet, Multifractal scaling of probability density function: a tool for turbulent data analysis, J. Phys. B 6 (1996) 937-943.
24. I.S. Gradshtein, I.M. Ryshik, Table of Integrals Series and Products. Academic Press, New York, 1994.