On the large time asymptotics of decaying Burgers turbulence

Communications in Mathematical Physics

Volumn 212, Issue 2, 2000, Pages 415-436

  Tribe, Roger ^a   Zaboronski, Oleg ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349029     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000214     Document Type: Review

References (35)

1. 1. Aurell, E., Frisch, U., Noullez, A., Blank, M.: Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity, chao-dyn/961101, published in J. Stat. Phys. 88, 1151-1164
2. 2. Avellaneda, M., Ryan, R., E, Weinan: PDFs for velocity and velocity gradients in Burgers' turbulence. Commun. Math. Phys. 172, no. 1, 13-38 (1995)
3. 3. Avellaneda, M., E, Weinan: Statistical properties of shocks in Burgers turbulence. Commun. Math. Phys. 172, no. 1, 13-38 (1995)
4. 4. Avellaneda, M.: Statistical properties of shocks in Burgers turbulence. II. Tail probabilities for velocities, shock-strengths and rarefaction intervals. Commun. Math. Phys. 169, no. 1, 45-59 (1995)
5. 5. Balkovsky, E., Falkovich, G., Kolokolov, I., Lebedev, V.: Intermittency of Burgers' Turbulence . Phys. Rev. Lett. 78, 1452 (1997)
6. 6. Balkovsky, E., Falkovich, G., Kolokolov, I., Lebedev, V.: Viscous Instanton for Burgers' Turbulence. Phys. Rev. Lett. 78, 1452 (1997)
7. 7. Balkovski, E. and Falkovich, G.: Private communication
8. 8. Bec, J., Frisch, U.: Pdf's of Derivatives and Increments for Decaying Burgers Turbulence. cond-mat/9906047
9. 9. Bernard, D. and Gawedzki, K.: Scaling and exotic regimes in the decaying Burgers turbulence. chao-dyn/9805002
10. 10. Borodin, A.N., Salminen, P.: Handbook of Brownian motion - facts and formulae. Probability and its Applications. Birkhäuser Verlag, Basel, 1996
11. 11. Burgers, J. M.: Statistical problems connected with the solution of a simple non-linear partial differential equation. I, II, III. Nederl. Akad. Wetensch. Proc. Ser. B. 57, 403-413, 414-424, 425-433 (1954)
12. 12. Falkovich, G.: Unpublished
13. 13. Frachebourg, L., Martin, Ph.A.: Exact statistical properties of the Burgers equation, cond-mat/9909056
14. 14. Frisch, U., Vergassola, M.: A prediction of the multifractal model: the intermediate dissipation range. In: New approaches and concepts in turbulence (Monte Verità, 1991), Basel: Birkhäuser, 1993, pp. 29-34
15. 15. Frisch, U.: Turbulence. The legacy of A. N. Kolmogorov. Cambridge: Cambridge University Press, 1995
16. 16. Gotoh, T. and Kraichnan, R.: Statistics of decaying Burgers turbulence. Phys. Fluids A 5, (2), (1993)
17. 17. Gurbatov, S.N.,Malakhov, A.N., Saichev, A.I.: Nonlinear random waves and turbulence in nondispersive media: Waves, rays, particles. Translated from the Russian. Supplement 1 by Adrian L. Melott and Sergei F. Shandarin. Supplement 2 by V. I. Arnol'd, Yu. M. Baryshnikov and I. A. Bogayevsky. Translation edited and with a preface by D. G. Crighton. Nonlinear Science: Theory and Applications. Manchester: Manchester University Press, 1991
18. 18. Gurbatov, S.N., Simdyankin, S.I., Aurell, E., Frisch, U., Tóth, G.: On the decay of Burgers turbulence. J. Fluid Mech. 344, 339-374 (1997)
19. 19. Gurarie, V., Migdal, A.: Instantons in Burgers Equation. Phys. Rev. E 54, 4908-4914 (1996)
20. xx.Comm. Pure Appl. Math. 3, 201-230 (1950)
21. 21. E. W., Khanin, K., Mazel, A., and Sinai, Ya.G. : Invariant measures for the random forced Burgers equation. Submitted to Ann. Math.
22. 22. E. W., Khanin, K., Mazel, A., and Sinai, Ya.G. Probability distribution functions for the random forced Burgers equation. Phys. Rev. Letters 78, 1904-1907 (1997)
23. 23. Kida, S.: Asymptotic properties of Burgers turbulence. J. Fluid Mech. 93 no. 2, 337-377 (1979)
24. 24. Kraichnan, R.H.: Note on Forced Burgers Turbulence. chao-dyn/9901023
25. 25. Kraichnan, R.: Unpublished
26. 26. Mehta, M.L.: Random matrices. Second edition. Boston, MA: Academic Press, Inc., 1991
27. 27. Parker, D.F.: The decay of sawtooth solutions to the Burgers equation. Proc. Roy. Soc. London Ser. A 369, no. 1738, 409-424 (1980)
28. 28. Polyakov, A.M.: Turbulence without pressure. Phys. Rev. E (3) 52, no. 6, part A, 6183-6188 (1995)
29. 29. Revuz, D. and Yor, M.: Continuous Martingales and Brownian Motion Berlin-Heidelberg-New York: Springer Verlag, 1991
30. 30. Rogers, L.C.G. and Williams, D.: Diffusions, Markov Processes, and Martingales. Volume 2. New York: Wiley, 1986
31. 31. Ryan, R., Avellaneda, M.: The one-point statistics of viscous Burgers turbulence initialized with Gaussian data. Commun. Math. Phys. 200, no. 1, 1-23 (1999)
32. 32. Sinai, Ya.G.: Statistics of shocks in solutions of inviscid Burgers equation. Commun. Math. Phys. 148, no. 3, 601-621 (1992)
33. 33. Truman, A., Zhao, H.Z.: On stochastic diffusion equations and stochastic Burgers' equations. J. Math. Phys. 37, no. 1, 283-307 (1996)
34. 34. Truman, A., Zhao, H.Z.: Stochastic Burgers' equations and their semi-classical expansions. Commun. Math. Phys. 194, 1, 231-248 (1998)
35. 35. E. W., Vanden Eijnden, E.: Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit. chao-dyn/9904028