Front speed enhancement in cellular flows

Chaos

Volumn 12, Issue 2, 2002, Pages 481-488

  Abel, M ^a,b   Cencini, M ^b,c   Vergni, D ^b,c   Vulpiani, A ^b,c  

^a UNIVERSITY OF POTSDAM   (Germany)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^c INFM   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036592446     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1457467     Document Type: Article

References (47)

1. J. Xin, "Front propagation in heterogeneous media," SIAM Rev. 42, 161 (2000).
2. F.A. Williams, Combustion Theory (Benjamin-Cummings, Menlo Park, 1985).
3. E.R. Abraham, "The generation of plankton patchiness by turbulent stirring," Nature (London) 391, 577 (1998); E.R. Abraham, C.S. Law, P.W. Boyd, S.J. Lavender, M.T. Maldonado, and A.R. Bowie, "Importance of stirring in the development of an iron-fertilized phytoplankton bloom," ibid. 407, 727 (2000).
4. E.R. Abraham, "The generation of plankton patchiness by turbulent stirring," Nature (London) 391, 577 (1998); E.R. Abraham, C.S. Law, P.W. Boyd, S.J. Lavender, M.T. Maldonado, and A.R. Bowie, "Importance of stirring in the development of an iron-fertilized phytoplankton bloom," ibid. 407, 727 (2000).
5. J. Ross, S.C. Müller, and C. Vidal, "Chemical waves," Science 240, 460 (1988); I.R. Epstein, "The consequences of imperfect mixing in autocatalytic chemical and biological systems," Nature (London) 374, 231 (1995).
6. J. Ross, S.C. Müller, and C. Vidal, "Chemical waves," Science 240, 460 (1988); I.R. Epstein, "The consequences of imperfect mixing in autocatalytic chemical and biological systems," Nature (London) 374, 231 (1995).
7. P.D. Ronney, "Some open issues in premixed turbulent combustion," in Modeling in Combustion Science, edited by J. Buckmaster and T. Takeno, Springer-Verlag Lecture Notes in Physics (Springer, New York, 1994), pp. 3-22.
8. N. Peters, Turbulent Combustion (Cambridge University Press, Cambridge, 2000).
9. P.D. Ronney, B.D. Haslam, and N.O. Rhys, "Front propagation rates in randomly stirred media," Phys. Rev. Lett. 74, 3804 (1995).
10. A.N. Kolmogorov, I.G. Petrovskii, and N.S. Piskunov, "Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem," Moscow Univ. Bull. Math. 1, 1 (1937); R.A. Fischer, "The wave of advance of advantageous genes," Ann. Eugenics 7, 355 (1937).
11. A.N. Kolmogorov, I.G. Petrovskii, and N.S. Piskunov, "Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem," Moscow Univ. Bull. Math. 1, 1 (1937); R.A. Fischer, "The wave of advance of advantageous genes," Ann. Eugenics 7, 355 (1937).
12. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989); A. Crisanti, M. Falcioni, G. Paladin, and A. Vulpiani, "Lagrangian chaos: Transport, mixing and diffusion in fluids," Riv. Nuovo Cimento 14, 1 (1991).
13. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989); A. Crisanti, M. Falcioni, G. Paladin, and A. Vulpiani, "Lagrangian chaos: Transport, mixing and diffusion in fluids," Riv. Nuovo Cimento 14, 1 (1991).
14. B. Audoly, H. Beresytcki, and Y. Pomeau, "Réaction diffusion en écoulement stationnaire rapide," C.R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 328, 255 (2000).
15. P. Constantin, A. Kiselev, A. Oberman, and L. Ryzhik, "Bulk burning rate in passive-reactive diffusion," Arch. Ration. Mech. Anal. 154, 53 (2000).
16. A. Kiselev and L. Ryzhik, "Enhancement of the traveling front speeds in reaction-diffusion equations with advection," Ann. I.H. Poincaré 18, 309 (2001).
17. T.H. Solomon and J.P. Gollub, "Chaotic particle transport in time-dependent Rayleigh-Bénard convection," Phys. Rev. A 38, 6280 (1988); "Passive transport in steady Raleigh-Bénard convection," Phys. Fluids 31, 1372 (1988).
18. T.H. Solomon and J.P. Gollub, "Chaotic particle transport in time-dependent Rayleigh-Bénard convection," Phys. Rev. A 38, 6280 (1988); "Passive transport in steady Raleigh-Bénard convection," Phys. Fluids 31, 1372 (1988).
19. M. Abel, A. Celani, D. Vergni, and A. Vulpiani, "Front propagation in laminar flows," Phys. Rev. E 64, 046307 (2001).
20. A.C. Marti, F. Sagues, and J.M. Sancho, "Front dynamics in turbulent media," Phys. Fluids 9, 3851 (1997); "Reaction-diffusion fronts under stochastic advection," Phys. Rev. E 56, 1729 (1997).
21. A.C. Marti, F. Sagues, and J.M. Sancho, "Front dynamics in turbulent media," Phys. Fluids 9, 3851 (1997); "Reaction-diffusion fronts under stochastic advection," Phys. Rev. E 56, 1729 (1997).
22. P.F. Embid, A.J. Majda, and P.E. Souganidis, "Comparison of turbulent flame speeds from complete averaging and the G-equation," Phys. Fluids 7, 2052 (1995).
23. A.R. Kerstein, W.T. Ashurst, and F.A. Williams, "Field equation for interface propagation in an unsteady homogeneous flow field," Phys. Rev. A 37, 2728 (1988).
24. M. Avellaneda and A. Majda, "Stieltjes integral representation and effective diffusivity bounds for turbulent transport," Phys. Rev. Lett. 62, 753 (1989); M. Avellaneda and M. Vergassola, "Stieltjes integral representation of effective diffusivities in time-dependent flows," Phys. Rev. E 52, 3249 (1995).
25. M. Avellaneda and A. Majda, "Stieltjes integral representation and effective diffusivity bounds for turbulent transport," Phys. Rev. Lett. 62, 753 (1989); M. Avellaneda and M. Vergassola, "Stieltjes integral representation of effective diffusivities in time-dependent flows," Phys. Rev. E 52, 3249 (1995).
26. W. Young, A. Pumir, and Y. Pomeau, "Anomalous diffusion of tracer in convection rolls," Phys. Fluids A 1, 462 (1989).
27. G. Boffetta, A. Celani, M. Cencini, G. Lacorata, and A. Vulpiani, "Non-asymptotic properties of transport and mixing," Chaos 10, 50 (2000).
28. M. Freidlin, Markov Processes and Differential Equations (Birkhauser, Boston, 1996).
29. S. Fedotov, "Scaling and renormalization for the Kolmogorov-Petrovskii-Piskunov equation with turbulent convection," Phys. Rev. E 55, 2750 (1997).
30. R.H. Kraichnan, "Turbulent diffusion: Evaluation of primitive and renormalized perturbation series by Padé approximations and by expansion of Stieltjes transforms into contributions from continuous orthogonal function," in The Padé Approximants in Theoretical Physics (Academic, New York, 1970), p. 129.
31. A.J. Majda and P.R. Kramer, "Simplified models for turbulent diffusion: Theory, numerical modeling and physical phenomena," Phys. Rep. 314, 237 (1999).
32. Y. Pomeau, "Dispersion dans un écoulement en présence de zones de recirculation," C.R. Acad. Sci. 301, 1323 (1985).
33. B.I. Shraiman, "Diffusive transport in Rayleigh-Bénard convection cell," Phys. Rev. A 36, 261 (1987).
34. M.N. Rosenbluth, A.L. Berk, I. Doxas, and W. Horton, "Effective diffusion in laminar convective flows," Phys. Fluids 30, 2636 (1987).
35. P. Constantin, A. Kiselev, and L. Ryzhik, "Quenching of flames by fluid advection," Commun. Pure Appl. Math. 54, 1320 (2001).
36. R.M. McLaughlin and J. Zhu, "The effect of finite front thickness on the enhanced speed of propagation," Combust. Sci. Technol. 129, 89 (1997).
37. W.T. Ashurst and G.I. Shivanshinsky, "On flame propagation through periodic flow fields," Combust. Sci. Technol. 80, 159 (1991).
38. R.C. Aldredge, "The scalar-field front propagation equation and its applications," in Modeling in Combustion Science, edited by J. Buckmaster and T. Takeno, Springer-Verlag Lecture Notes in Physics (Springer, New York, 1994), pp. 23-35.
39. R.C. Aldredge, "Premixed flame propagation in a high-intensity, large-scale vortical flow," Condens. Matter Phys. 106, 29 (1996).
40. M. Cencini, A. Torcini, D. Vergni, and A. Vulpiani, "Thin front propagation in steady and unsteady cellular flows" (LANL e-print archive nlin/ 0201015).
41. V. Yakhot, "Propagation velocity of premixed turbulent flame," Combust. Sci. Technol. 60, 191 (1988).
42. M. Chertkov and V. Yakhot, "Propagation of a Huygens front through turbulent medium," Phys. Rev. Lett. 80, 2837 (1998).
43. A. Oberman, Ph.D. thesis, University of Chicago, 2001.
44. A.R. Kerstein and W.T. Ashurst, "Propagating rate of growing interfaces in stirred fluids," Phys. Rev. Lett. 68, 934 (1992).
45. W.T. Ashurst, "Flame propagation through swirling eddies, a recursive pattern," Combust. Sci. Technol. 92, 87 (1993).
46. V. Petrov, Q. Ouyang, and H.L. Swinney, "Resonant pattern formation in a chemical system," Nature (London) 388, 655 (1997); M. Dolnik, A.M. Zhabotinsky, and I.R. Epstein, "Resonant suppression of Turing patterns by periodic illumination," Phys. Rev. E 63, 026101 (2001).
47. V. Petrov, Q. Ouyang, and H.L. Swinney, "Resonant pattern formation in a chemical system," Nature (London) 388, 655 (1997); M. Dolnik, A.M. Zhabotinsky, and I.R. Epstein, "Resonant suppression of Turing patterns by periodic illumination," Phys. Rev. E 63, 026101 (2001).