Global picture of self-similar and non-self-similar decay in Burgers turbulence

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 5, 2005, Pages

  Noullez, Alain ^a   Gurbatov, Sergey N ^b   Aurell, Erik ^c   Simdyankin, Sergey I ^d  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

^c ALBANOVA UNIVERSITY CENTER   (Sweden)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC THEORY; WAVE NUMBER;

COMPUTER SIMULATION; DYNAMICS; NATURAL FREQUENCIES; SPECTRUM ANALYSIS;

GAUSSIAN NOISE (ELECTRONIC);

EID: 27144527957     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.056305     Document Type: Article

References (33)

1. J. Burgers, The Nonlinear Diffusion Equation (Reidel, Dordrecht, 1974).
2. G. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
3. O. Rudenko and S. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Plenum Press, New York, 1977).
4. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin, 1985).
5. S. Gurbatov, A. Malakhov, and A. Saichev, Nonlinear Random Waves and Turbulence in Nondispersive media: Waves, rays, particles (Manchester University Press, Manchester, 1991).
6. W. Woyczynski, Burgersâ€"KPZ Turbulence: Gottingen Lectures (Springer-Verlag, New York, 1998).
7. S. Gurbatov, A. Saichev, and S. Shandarin, Mon. Not. R. Astron. Soc. MNRAA4 0035-8711 236, 385 (1989).
8. S. Shandarin and Y. Zelâdovich, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.61.185 61, 185 (1989).
9. M. Vergassola, B. Dubrulle, U. Frisch, and A. Noullez, Astron. Astrophys. AAEJAF 0004-6361 289, 325 (1994).
10. Y. Sinai, Commun. Math. Phys. CMPHAY 0010-3616 148, 601 (1992).
11. Z. She, E. Aurell, and U. Frisch, Commun. Math. Phys. CMPHAY 0010-3616 148, 623 (1992).
12. M. Schwartz and S. Edwards, Europhys. Lett. EULEEJ 0295-5075 20, 301 (1992).
13. M. Kardar, G. Parisi, and Y. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.889 56, 889 (1986).
14. A.-L. BarabÃisi and H. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995).
15. L. Frachebourg and P. A. Martin, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112000001142 417, 323 (2000).
16. G. Molchan, J. Stat. Phys. JSTPBS 0022-4715 88, 1139 (1997).
17. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, England, 1995).
18. S. Gurbatov, S. Simdyankin, E. Aurell, U. Frisch, and G. Toth, J. Fluid Mech. JFLSA7 0022-1120 344, 349 (1997).
19. A. Kolmogorov, Dokl. Akad. Nauk SSSR DANKAS 0002-3264 31, 538 (1941).
20. L. Loitsyansky, Trudy Tsentr. Aero.-Gidrodin. Inst pp. 3â€"23 (1939).
21. G. Eyink and D. Thomson, Phys. Fluids PHFLE6 1070-6631 10.1063/1.870279 12, 477 (2000).
22. E. Hopf, Commun. Pure Appl. Math. CPMAMV 0010-3640 3, 201 (1950).
23. J. Cole, Q. Appl. Math. QAMAAY 0033-569X 9, 225 (1951).
24. S. Kida, J. Fluid Mech. JFLSA7 0022-1120 93, 337 (1979).
25. S. Gurbatov and A. Saichev, Sov. Phys. JETP SPHJAR 0038-5646 53, 347 (1981).
26. J. D. Fournier and U. Frisch, J. Mec. Theor. Appl. JMTADB 0750-7240 2, 699 (1983).
27. S. Molchanov, D. Surgailis, and W. Woyczynski, Commun. Math. Phys. CMPHAY 0010-3616 168, 209 (1995).
28. M. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes (Springer, Berlin, 1983).
29. S. Gurbatov and A. Malakhov, Sov. Phys. Acoust. SOPAAX 0038-562X 23, 325 (1977).
30. M. Avellaneda and W. E, Commun. Math. Phys. CMPHAY 0010-3616 172, 13 (1995).
31. E. Aurell, S. Gurbatov, and I. Wertgeim, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93)90062-5 182, 109 (1993).
32. S. Gurbatov and G. Pasmanik, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/1.558798 88, 309 (1999).
33. A. Noullez and M. Vergassola, J. Sci. Comput. JSCOEB 0885-7474 10.1007/BF01575032 9, 259 (1994).