Dispersion and collapse in stochastic velocity fields on a cylinder

Journal of Statistical Physics

Volumn 138, Issue 4, 2010, Pages 579-597

  Celani, Antonio ^a   Rubenthaler, Sylvain ^b   Vincenzi, Dario ^b  

^a INSTITUT PASTEUR   (France)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Cylindrical manifolds; Kraichnan ensemble; Lagrangian trajectories; Turbulence

Indexed keywords

EID: 77249125798     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9875-1     Document Type: Article

References (30)

1. Bernard, D., Boffetta, G., Celani, A., Falkovich, G.: Conformal invariance in two-dimensional turbulence. Nat. Phys. 2, 124-128 (2006).
2. Boffetta, G., Celani, A., Vergassola, M.: Inverse energy cascade in two-dimensional turbulence: deviations from Gaussian behavior. Phys. Rev. E 61, R29-R32 (2000).
3. Chertkov, M., Kolokolov, I., Vergassola, M.: Inverse versus direct cascades in turbulent advection. Phys. Rev. Lett. 80, 512-515 (1998).
4. Chetrite, R., Delannoy, J. Y., Gawȩdzki, K.: Kraichnan flow in a square: An example of integrable chaos. J. Stat. Phys. 126, 1165-1200 (2007).
5. Da Prato, G., Zabczyk, J.: Ergodicity for Infinite Dimensional Systems. London Mathematical Society Lecture Note Series, vol. 229. Cambridge University Press, Cambridge (1996).
6. Dudley, R.: Real Analysis and Probability. Wadsworth and Brooks, Belmont (1989).
7. Doob, J. L.: Asymptotic properties of Markoff transition probabilities. Trans. Am. Math. Soc. 63, 393-421 (1948).
8. E, W., Vanden Eijnden, E.: Generalized flows, intrinsic stochasticity, and turbulent transport. Proc. Natl. Acad. Sci. USA 97, 8200-8205 (2000).
9. Erdélyi, A. (ed.): Higher Transcendental Functions. McGraw-Hill, Malabar (1953).
10. Fannjiang, A. C.: Convergence of passive scalar fields in Ornstein-Uhlenbeck flows to Kraichnan's model. J. Stat. Phys. 114, 115-135 (2004).
11. Falkovich, G., Gawȩdzki, K., Vergassola, M.: Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913-975 (2001).
12. Fournier, J. D., Frisch, U.: d-dimensional turbulence. Phys. Rev. A 17, 747-762 (1978).
13. Frisch, U.: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1995).
14. Gawȩdzki, K., Horvai, P.: Sticky behavior of fluid particles in the compressible Kraichnan model. J. Stat. Phys. 116, 1247-1300 (2004).
15. Gawȩdzki, K., Vergassola, M.: Phase transition in the passive scalar advection. Physica D 138, 63-90 (2000).
16. Giuliani, P., Jensen, M. H., Yakhot, V.: Critical "dimension" in shell model turbulence. Phys. Rev. E 65, 036305 (2002).
17. Khas'minskii, R. Z.: Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equations. Theory Probab. Appl. 5, 179-196 (1960).
18. Kraichnan, R. H.: Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417-1423 (1967).
19. Kraichnan, R. H.: Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945-963 (1968).
20. Le Jan, Y., Raimond, O.: Solutions statistiques fortes des équations différentielles stochastiques. C. R. Acad. Sci. Paris Sér. I 327, 893-896 (1998).
21. Le Jan, Y., Raimond, O.: Integration of Brownian vector fields. Ann. Probab. 30, 826-876 (2002).
22. Le Jan, Y., Raimond, O.: Flows, coalescence and noise. Ann. Probab. 32, 1247-1315 (2004).
23. Le Jan, Y., Raimond, O.: Stochastic flows on the circle. In: Waymire, E. C., Duan, J. (eds.) Probability and Partial Differential Equations in Modern Applied Mathematics. The IMA Volumes in Mathematics and Its Applications, vol. 140, pp. 151-162. Springer, New York (2005).
24. L'vov, V. S., Pomyalov, A., Procaccia, I.: Quasi-Gaussian statistics of hydrodynamic turbulence in 4/3+ε dimensions. Phys. Rev. Lett. 89, 064501 (2002).
25. Monin, A. S., Yaglom, A. M.: Statistical Fluid Mechanics, vol. 2. MIT Press, Cambridge (1975).
26. Pagès, G.: Sur quelques algorithmes récursifs pour les probabilités numériques. ESAIM: Probab. Stat. 5, 141-170 (2001).
27. Rogers, L. C. G., Williams, D.: Diffusions, Markov Processes, and Martingales. Cambridge University Press, Cambridge (1979).
28. Stroock, D. W., Varadhan, S. R. S.: Multidimensional Diffusion Processes. Springer, New York (1979).
29. Skorokhod, A. V.: Asymptotic Methods in the Theory of Stochastic Differential Equations. Translations of Mathematical Monographs, vol. 78. American Mathematical Society, Providence (1989).
30. Vergassola, M., Mazzino, A.: Structures and intermittency in a passive scalar model. Phys. Rev. Lett. 79, 1849-1852 (1997).