Coupled KS-CGL and coupled Burgers-CGL equations for flames governed by a sequential reaction

Physica D: Nonlinear Phenomena

Volumn 129, Issue 3-4, 1999, Pages 253-298

  Golovin, A A ^a,b   Matkowsky, B J ^a   Bayliss, A ^a   Nepomnyashchy, A A ^b  

^a Northwestern University   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000573274     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00318-2     Document Type: Article

References (44)

1. Y.B. Zeldovich, G.I. Barenblatt, V.B. Librovich, G.M. Makhviladze, The Mathematical Theory of Combustion and Explosion, Consultants Bureau, New York, 1985.
2. F.A. Williams, Combustion Theory, Benjamin Cummings, Menlo Park, 1985.
3. J.D. Buckmaster, G.S.S. Ludford, Theory of Laminar Flames, Cambridge University Press, Cambridge, 1982.
4. G.I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames I. Derivation of basic equations, Acta Astronautica 4 (1977) 1177.
5. D.O. Olagunju, B.J. Matkowsky, Coupled complex Ginzburg-Landau type equations in gaseous combustion, Stability Appl. Ana. Continu. Media 2 (1992) 31.
6. B.I. Khaikin, A.K. Filonenko, S.I. Khudyaev, Flame propagation in the presence of two successive gas phase reactions, Combust. Explosion Shock Waves 4 (1968) 343.
7. V.S. Berman, Yu.S. Ryazantsev, Asymptotic analysis of stationary propagation of the front of a two-stage exothermic reaction in a gas, J. Appl. Math. Mech. (PMM) 37 (1973) 995.
8. G. Joulin, P. Clavin, Asymptotic analysis of a premixed laminar flame governed by a two-step reaction, Combust. Flame 25 (1975) 389.
9. A. Kapila, G.S.S. Ludford, Two-step sequential reactions for large activation energies, Combust. Flame 29 (1977) 167.
10. S.B. Margolis, B.J. Matkowsky, Steady and pulsating modes of sequential flame propagation, Comb. Sci. Technol. 27 (1982) 193.
11. J. Pelaez, A. Linan, Structure and stability of flames with two sequential reactions, SIAM J. Appl. Math. 45 (1985) 503.
12. J. Pelaez, Stability of premixed flames with two thin reaction layers, SIAM J. Appl. Math. 47 (1987) 781.
13. A.R. Burgess, C.J. Langley, The chemical structure of premixed fuel-rich methane flames: the effect of hydrocarbon species in the secondary reaction zone, Proc. Roy. Soc. Lond. A 433 (1991) 1.
14. P. Gray, A.R. Hall, H.G. Wolfhard, Stationary flames of methyl nitrate and methyl nitrite, Proc. Roy. Soc. Lond. A 232 (1955) 389.
15. R.M. Fristrom, A.A. Westenberg, Flame Structure, McGraw Hill, New York, 1965.
16. A. Friedman, E. Burke, Measurement of temperature distribution in a low-pressure flat flame, J. Chem. Phys. 22 (1954) 824.
17. C.S. Raymond, private communication.
18. H. Kidachi, On mode interactions in reaction diffusion equation with nearly degenerate bifurcations, Prog. Theor. Phys. 63 (1980) 1152.
19. J.J. Perraud, A.De Wit, E. Dulos, RDe Kepper, G. Dewel, P. Borckmans, One-dimensional "spirals": novel asynchronous chemical wave source, Phys. Rev. Lett. 71 (1993) 1272.
20. R.J. Braun, G.J. Merchant, S.H. Davis, Pulsatile and cellular mode interaction in rapid directional solidification, Phys. Rev. B 45 (1992) 7002.
21. K. Fujimura, YY Renardy, The 2/1 steady Hopf mode interaction in the two-layer Benard problem, Physica D 85 (1995) 25.
22. P. Colinet, P. Georis, J.C. Legros, G. Lebon, Spatially quasiperiodic convection and temporal chaos in two-layer thermocapillary instabilities, PRE 54 (1996) 514.
23. B.J. Matkowsky, G.I. Sivashinsky, An asymptotic derivation of two models in flame theory associated with the constant density approximation, SIAM J. Appl. Math. 37 (1979) 686.
24. M.R. Booty, S.B. Margolis, B.J. Matkowsky, Interaction of pulsating and spinning waves in nonadiabatic flame propagation, SIAM J. Appl. Math. 47 (1987) 1241.
25. A.A. Nepomnyashchy, Order parameter equations for long wavelength instabilities, Physica D 86 (1995) 90.
26. A. Zippelius, E.D. Siggia, Disappearance of stable convection between free slip boundaries, Phys. Rev. A 26 (1982) 1788.
27. A.J. Bernoff, Finite amplitude convection between stress-free boundaries; Ginzburg-Landau equations and modulation theory, Eur. J. Appl. Math. 5 (1994) 267.
28. M. Renardy, Y Renardy, Derivation of amplitude equations and analysis of sideband instabilities in two layer flows, Phys. Fluids A 5 (1993) 2738.
29. P. Barthelet, F. Charru, Benjamin-Feir and Eckhaus instabilities with Galilean invariance: the case of interfacial waves in viscous shear flows, Eur. J. Mech. B/Fluids 17 (1998) 1.
30. I.B. Ponomarenko, On stability of three-dimensional periodic motions in hydrodynamics, J. Appl. Math. Mech. (PMM) 37 (1973) 990.
31. A.C. Newell, Envelope equations, Lectures in applied mathematics, Am. Math. Soc. Providence RI 15 (1974) 157.
32. J.M. Hyman, B. Nicolaenko, The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems, Physica D 18 (1986) 113.
33. J.M. Hyman, B. Nicolaenko, Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces, Physica D 23 (1986) 265.
34. I.G. Kevrekidis, B. Nicolaenko, J.C. Scovel, Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math. 50 (1990) 760.
35. H.S. Brown, I.G. Kevrekidis, Modulated traveling waves for the Kuramoto-Sivashinsky equation, Fields Inst. Comm. 5 (1996) 45.
36. K. Nozaki, N. Bekki, Exact solutions of the generalized Ginzburg-Landau equation, J. Phys. Soc. Japan 53 (1984) 1581.
37. N. Bekki, K. Nozaki, Formation of spatial patterns and holes in the generalized Ginzburg-Landau equation, Phys. Lett. A 110 (1985) 133.
38. H. Chate, Spatio-temporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation, Nonlinearity 7 (1994) 185.
39. A.A. Nepomnyashchy, Three-dimensional spatially periodic motions in a liquid film flowing down a vertical plane, in: E.M. Zhukhovitsky (Ed.), Fluid Dynamics, pt. 7, vol. 43-52, Perm, 1974 (in Russian).
40. A.A. Nepomnyashchy, On nonstationary wavy flows in a liquid film flowing down a vertical plane, in: G.Z. Gershuni, E.M. Zhukhovitsky, B.I. Myznikova (Eds.), Processes of Heat and Mass Transfer in Viscous Fluids, vol. 25-32, Ural Branch Acad. Sci. USSR, Sverdlovsk, 1986 (in Russian).
41. G. Dangelmayr, F. Knobloch, M. Wegelin, Dynamics of traveling waves in finite containers, Europhys. Lett. 16 (1991) 723.
42. C. A. Pereira, J.M. Vega, On the pulsating instability of two-dimensional flames, Eur. J. Appl. Math. 3 (1992) 55.
43. B.J. Matkowsky, V.A. Volpert, Coupled nonlocal complex Ginzburg-Landau equations in gasless combustion, Physica D 54 (1992) 203.
44. A. Bernoff, R. Kuske, B.J. Matkowsky, V.A. Volpert, Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems, SIAM J. Appl. Math. 55 (1995) 485.