Advection of passive and reactive tracers in multi-dimensional Burgers' velocity field

Physica D: Nonlinear Phenomena

Volumn 100, Issue 1-2, 1997, Pages 119-141

  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

Burgers' turbulence; Passive tracer transport; Reaction diffusion equation; Turbulent diffusion

Indexed keywords

EID: 4243315309     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)81280-8     Document Type: Article

References (28)

1. M. Avellaneda and E. Weinan, Statistical properties of shocks in Burgers turbulence, Comm. Math. Phys. 172 (1995) 13-38.
2. J.M. Burgers, The Nonlinear Diffusion Equation (Reidel, Dordrecht, 1974).
3. R. Carmona and J. Lacroix, Spectral Theory of Random Schrödinger Operators (Birkhäuser, Boston, 1990).
4. G.T. Csanady, Turbulent Diffusion in the Environment (Reidel, Dordrecht, 1980).
5. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1996).
6. T. Funaki, D. Surgailis and W.A. Woyczynski, Gibbs-Cox random fields and Burgers' turbulence, Ann. Appl. Probab. 5 (1995) 701-736.
7. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin, 1985).
8. S. Gurbatov, A. Malakhov and A. Saichev, Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays and Particles (Manchester, University Press, Manchester, 1991).
9. L. Hörmander, The Analysis of Linear Partial Differential Operators I (Springer, Berlin, 1983).
10. Y. Hu and W.A. Woyczynski, Shock density in Burgers' turbulence, in: Nonlinear Stochastic PDEs: Burgers Turbulence and Hydrodynamic Limit, eds. T. Funaki and W.A. Woyczynski, IMA Vol. 77 (Springer, Berlin, 1995) pp. 211-226.
11. S. Kida, Asymptotic properties of Burgers turbulence, J. Fluid Mech. 93 (1979) 337-377.
12. V. Klyatskin, W.A. Woyczynski and D. Gurarie, Diffusing passive tracers in random incompressible flows: Statistical topography aspects, J. Statist. Phys. 84 (3/4) (1996) 797-836.
13. L. Kofman, D. Pogosyan, S. Shandarin and A. Melott, Coherent structures in the Universe and the adhesion model, Astrophys, J. 393 (1992) 437-449.
14. R.H. Kraichnan, Lagrangian-history statistical theory for Burgers' equation, Phys. Fluids 11 (1968) 265-277.
15. R.H. Kraichnan, Models of intermittency in hydrodynamic turbulence, Phys. Rev. Lett. 65 (1990) 575-578.
16. P.D. Lax, The zero dispersion limit, a deterministic analogue of turbulence, Comm. Pure Appl. Math. 44 (1991) 1047-1056.
17. P.D. Lax and C.D. Levermore, The small dispersion limit of the Korteveg-de Vries equation, Commun. Pure Appl. Math. 36 (1983); I, 253-290; II, 571-593; III, 809-829.
18. S.A. Molchanov, D. Surgailis and W.A. Woyczynski, Hyperbolic asymptotics in Burgers' turbulence and extremal processes, Commun. Math. Phys. 168 (1995) 209-226.
19. A.I. Saichev and W.A. Woyczynski, Density fields in Burgers and KdV-Burgers turbulence, SIAM J. Appl. Math. 56 (4) (1996) 1-31.
20. V. Sashi, B.S. Sathuarprakash and S.F. Shandarin, The evolution of voids in the adhesion approximation, Astrophys. J. 431 (1994) 20-40.
21. S.F. Shandarin and B.Z. Zeldovich, Turbulence, intermittency, structures in a self-gravitating medium: the large scale structure of the Universe, Rev. Modern Phys. 61 (1989) 185-220.
22. Z.-S. She, E. Aurell and U. Frisch, The inviscid Burgers equation with initial data of Brownian type, Commun. Math. Phys. 148 (1992) 623-641.
23. Ya.G. Sinai, Statistics of shocks in solutions of inviscid Burgers equation, Commun. Math. Phys. 148 (1992) 601-621.
24. J. Smoller, Shock Waves and Reaction-Diffusion Equations (Springer, Berlin, 1994).
25. N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1985).
26. D.H. Weinberg and J.E. Gunn, Large scale structure and the adhesion approximation, Monthly Not. Royal Astronom. Soc. 247 (1990) 260-286.
27. M. Vergassola, B. Dubrulles, U. Frisch and A. Noullez, Burgers' equation, devil's staircases and the mass distribution for large-scale structures, Astronom. Astrophys. Ser. 289 (1994) 325-356.
28. W.A. Woyczynski, Stochastic Burgers' flows, in: Nonlinear Waves and Weak Turbulence, eds. N. Fitzmaurice et al. (Birkhäuser, Boston, 1993) pp. 279-311.