Absolute and convective instabilities, front velocities and global modes in nonlinear systems

Physica D: Nonlinear Phenomena

Volumn 108, Issue 3, 1997, Pages 236-276

  Couairon, Arnaud ^a   Chomaz, Jean Marc ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001435082     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00045-6     Document Type: Article

References (39)

1. P. Huerre and P.A. Monkewitz, Local and global instabilities in spatially developing flows, Ann. Rev. Fluid Mech. 22 (1990) 473.
2. A. Bers, in: Physique des Plasmas, eds. C. DeWitt and J. Peyraud (Gordon and Breach, New York, 1975).
3. M.C. Cross and P.C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65 (1993) 851.
4. J.M. Chomaz, P. Huerre and L.G. Redekopp, Bifurcations to local and global modes in spatially developing flows, Phys. Rev. Lett. 60 (1988) 25.
5. J.M. Chomaz, P. Huerre and L.G. Redekopp, The effect of nonlinearity and forcing on global modes, in: New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena, eds. P. Coullet and P. Huerre (Plenum Press, New York, 1990).
6. J.M. Chomaz, P. Huerre and L.G. Redekopp, A frequency selection criterion in spatially developing flows, Stud. Appl. Math. 84 (1991) 119.
7. P.A. Monkewitz, P. Huerre and J.M. Chomaz, Global linear stability analysis of weakly non parallel shear flows, J. Fluid Mech. 251 (1993) 1.
8. S. Le Dizès, P. Huerre, J.M. Chomaz and P.A. Monkewitz, Linear global modes in spatially developing media, Phil. Trans. R. Soc. Lond. A 354 (1996) 169.
9. R.E. Hunt, Spatially varying flows with localized forcing, Ph.D. Thesis.
10. R.E. Hunt and D.G. Crighton, Instability of flows in spatially developing media, R. Soc. Lond. A 435, 109.
11. K.R. Sreenivasan, S. Raghu and D. Kyle, Absolute instability in variable density round jets, Exp. Fluids 7 (1989) 309.
12. P.J. Strykowski and D.L. Niccum, The influence of velocity and density ratio on the dynamics of spatially developing mixing layers, Phys. Fluids A 4 (1992) 770.
13. S. Le Dizès, P. Huerre, J.M. Chomaz and P.A. Monkewitz, Nonlinear stability analysis of slowly diverging flows: Limitations of the weakly nonlinear approach, in: Proc. IUTAM Symp. on bluff-body wakes, dynamics and instabilities, eds. H. Eckelmann, J.M.R. Graham, P. Huerre and P.A. Monkewitz (Springer, Berlin, 147).
14. J.M. Chomaz, Absolute and convective instabilities in nonlinear systems, Phys. Rev. Lett. 69 (1992) 1931.
15. G. Dee, Dynamical properties of propagating front solutions of the amplitude equations, Physica D 15 (1985) 295.
16. G. Dee, Propagation into an unstable state, J. Statist. Phys. 39 (1985) 705.
17. E. Ben-Jacob, H. Brand, G. Dee, L. Kramer and J.S. Langer, Pattern propagation in nonlinear dissipative systems, Physica D 14 (1985) 348.
18. W. van Saarloos and P.C. Hohenberg, Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations, Physica D 56 (1992) 303.
19. W. van Saarloos, Front propagation into unstable states: Marginal stability as a dynamical mechanism for velocity selection, Phys. Rev. A 37 (1988) 211.
20. W. van Saarloos, Front propagation into unstable states. II. Linear versus nonlinear marginal stability and rate of convergence, Phys. Rev. A 39 (1989) 6367.
21. A. Couairon and J.M. Chomaz, Global Instability in fully nonlinear systems, Phys. Rev. Lett. 77 (1996) 4015.
22. J. Fineberg and V. Steinberg, Vortex-front propagation in Rayleigh-Benard convection, Phys. Rev. Lett. 58 (1987) 1332.
23. G. Ahlers and D.S. Cannel, Vortex-front propagation in rotating Couette-Taylor flow, Phys. Rev. Lett. 50 (1983) 1583.
24. M. Lücke, M. Mihelcic and K. Wingerath, Front propagation and pattern formation of Taylor vortices growing into unstable circular Couette flow, Phys. Rev. A 31 (1985) 396.
25. A. Hanna, A. Saul and K. Showalter, Detailed studies of propagating fronts in the iodate oxydation of arsenous acid, J. Am. Chem. Soc. 104 (1982) 3838.
26. D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978) 33.
27. P. Palffy-Muhoray, H.J. Yuan, B.J. Frisken and W. van Saarloos, in: Nonlinear Evolution of Spatio-temporal Structures in Dissipative Continuous Systems, eds. F.H. Busse and L. Kramer (Plenum Press, New York, 1990).
28. J.D. Gunton, M. San Miguel and P.S. Sahni, The dynamics of first-order phase transitions, in: Phase Transitions and Critical Phenomena, eds. C. Domb and J.L. Lebowitz, Vol. 8 (Academic Press, New York, 1983).
29. J.A. Powell, A.C. Newell and C.K.R.T. Jones, Competition between generic and nongeneric fronts in envelope equations, Phys. Rev. A 44 (1991) 3636.
30. C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
31. P. Coullet, L. Gil and D. Repaux, Defects and subcritical bifurcations, Phys. Rev. Lett. 62 (1989) 2957.
32. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York).
33. V. Hakim, in: Hydrodynamics and nonlinear instabilities, Cambridge University Press, to be published.
34. A. Couairon and J.M. Chomaz, Pattern selection in the presence of a cross flow, Phys. Rev. Lett., submitted.
35. P. Büchel, M. Lücke, D. Roth and R. Schmitz, Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow, Phys. Rev. E. 53 (1996) 4764.
36. H.W. Müller, M. Lücke and M. Kamps, Convective Patterns in Horizontal flow, Europhys. Lett. 10 (1989) 451;
37. Transversal convection patterns in horizontal shear flow, Phys. Rev. A 45 (1992) 3714.
38. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983).
39. D.G. Aronson and H.F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve propagation, in: Partial Differential Equations and Related Topics, Lecture Notes in Mathematics, Vol. 446 (Springer, New York, 1975) pp. 5-49.