Evolution of Burgers' turbulence in the presence of external forces

Journal of Fluid Mechanics

Volumn 331, Issue , 1997, Pages 313-343

  Saichev, A I ^a   Woyczynski, W A ^b  

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

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FLOW OF FLUIDS; HYDRODYNAMICS; MATHEMATICAL MODELS; STATISTICAL MECHANICS;

BURGERS TURBULENCE; VISCOUS DISSIPATION;

TURBULENCE;

FORCES; TURBULENCE;

EID: 0030917609     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096003953     Document Type: Article

References (35)

1. BERTINI, L., CANCRINI, N. & JONA-LASINIO, G. 1994 The stochastic Burgers equation. Commun. Math. Phys. 165, 211-232.
2. BURGERS, J. 1974 The Nonlinear Diffusion Equation. D. Reidel.
3. CARMONA, R. & LACROIX, J. 1990 Spectral Theory of Schrödinger Operators. Birkhäuser-Boston.
4. DA PRATO, G. & ZABCZYK, J. 1992 Stochastic Equations in Infinite Dimension. Cambridge University, Press.
5. DONSKER, M. D. 1964 On function space integrals. In Analysis in Function Space (ed. W. T. Martin & I. Segal), pp. 17-30. MIT Press.
6. FUNAKI, T. & SURGAILIS, D. & WOYCZYNSKI, W. A. 1995 Gibbs-Cox random fields and Burgers' turbulence. Ann. Appl. Probability 5, 701-735.
7. FURUTSU, K. 1963 On the statistical theory of electromagnetic waves in a fluctuating media. J. Res. Natl Bur. Stand. D-67, 303.
8. GURBATOV S., MALAKHOV A. & SAICHEV A. 1991 Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays and Particles. Manchester University Press.
9. GURBATOV, S. & SAICHEV, A. 1993 Inertial nonlinearity and chaotic motion of particle fluxes. Chaos 3, 333-358.
10. HANDA, K. 1995 On a stochastic PDE related to Burgers' equation with noise. In Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulence (ed. T. Funaki & W. A. Woyczynski). IMA Vol. 77, pp. 147-156. Springer.
11. HOLDEN, H., LINDSTRÖM, T., ØKSENDAL, B., UBØE, J. & ZHANG, T.-S. 1994 The Burgers equation with a noisy force and the stochastic heat equation. Commun. Partial Diff. Equat. 19, 119-141.
12. HU, Y. & WOYCZYNSKI, W. A. 1994 An extremal rearrangement property of statistical solutions of Burgers' equation. Ann. Appl. Probability 4, 338-358.
13. HU, Y. & WOYCZYNSKI, W. A. 1995 A maximum principle for unimodal moving average data for Burgers' equation. Probability and Math. Statist. 15, 153-171.
14. JANICKI, A., SURGAILIS, D. & WOYCZYNSKI, W. A. 1995 Statistics and geometric thermodynamics of passive tracer densities in 2-D forced Burgers turbulence. CWRU preprint.
15. KLVATSKIN, V. I, WOYCZYNSKI, W. A. & GURARIE, D. 1996a Short-time correlation approximations for diffusing tracers in random velocity fields: a functional approach. In Stochastic Modelling in Physical Oceanography (ed. R. Adler et al.), pp. 221-270. Birkhäuser-Boston.
16. KLYATSKIN, V. L, WOYCZYNSKI, W. A. & GURARIE, D. 1996b Diffusing passive tracers in random incompressible flows: statistical topography aspects. J. Statist. Phys. 84, 797-836.
17. KRAICHNAN, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers, J. Fluid Mech. 5, 497-543.
18. KAAICHNAN, R. H. 1968 Lagrangian-history statistical theory for Burgers' equation. Phys. Fluids 11, 265-277.
19. LIONS, P. A. 1982 Generalized Solutions of Hamilton-Jacobi Equation. Pitman.
20. MOLCHANOV, S. A., SURGAILIS, D. & WOYCZYNSKI, W. A. 1995a Hyperbolic asymptotics in Burgers' turbulence and extremal processes. Commun. Math. Phys. 168, 209-226.
21. MOLCHANOV, S. A., SURGAILIS, D. & WOYCZYNSKI, W. A. 1995b Spectral methods in analysis of forced Burgers turbulence. CWRU preprint.
22. d. Ann. Appl. Probability, to appear.
23. NAKAZAWA, H. 1980 Probabilistic aspects of equation of motion of forced Burgers and Navier-Stokes turbulence. Prog. Theor. Phys. 64, 1551-1564.
24. NOVIKOV, E. A. 1964 Functionals and the random-force method in turbulence theory. Sov. Phys. JETP 20(5), 1290.
25. OLEINIK, O. 1957 Discontinuous solutions of nonlinear differential equations. Russ. Math. Survey, Am. Math. Transl. Series 2, 26, 95-172
26. SAICHEV, A. I., WOYCZYNSKI, W. A. 1996a Distributions in the Physical and Engineering Sciences, vols 1 and 2. Birkhäuser-Boston, to appear.
27. SAICHEV, A. I. & WOYCZYNSKI, W. A. 1996b Model description of passive tracer density fields in the framework of Burgers' and other related model equations. In Nonlinear Stochastic PDE's:Burgers Turbulence and Hydrodynamic Limit. IMA Vol. 77, pp. 167-192. Springer.
28. SAICHEV, A. I. & WOYCZYNSKI, W. A. 1996c Density fields in Burgers' and KdV-Burgers' turbulence. SIAM J. Appl. Maths 56(4), 1-31.
29. SAHNI, V., SATHYAPRAKASH, B. S. & SHANDARIN, S. F. 1994 The evolution of voids in the adhesion approximation. Astrophys. J. 431, 20-40.
30. SINAI, YA. 1991 Two results concerning asymptotic behavior of solution of the Burgers equation with force. J. Statist. Phys. 64, 1-12.
31. SINAI, YA. 1996 Burgers system driven by a periodic stochastic flow. Princeton University preprint, 9pp.
32. SHANDARIN, S. F. & ZELDOVICH, YA. B. 1989 Turbulence, intermittency, structures in a self-gravitating medium: the large scale structure of the Universe. Rev. Mod. Phys. 61, 185-220.
33. SURGAILIS, D. & WOYCZYNSKI, W. A. 1994 Scaling limits of solutions of Burgers' equation with singular Gaussian initial data. In Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications, pp. 140-162. CRC Press,
34. TATSUMI, T. & KIDA, S. 1972 Statistical mechanics of the Burgers model of turbulence. J Fluid Mech. 55, 659-675.
35. YAKUSHKIN, I. G. 1981 Description of turbulence in the Burgers model. Radiophys. Quantum Electron. 24, 41-48.