Global and absolute instabilities of spatially developing open flows and media with algebraically decaying tails

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2034, 2003, Pages 1403-1425

  Brevdo, Leonid ^a  

^a AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Absolute instability; Algebraically decaying tails; Frequency selection mechanism; Global dispersion relations; Global instability; Open spatially developing flows and media

Indexed keywords

ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICS; OSCILLATION; PHYSICS; THEORETICAL STUDY;

EID: 1542512382     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.1087     Document Type: Article

References (35)

1. Batchelor, G. K. 2000 An introduction to fluid dynamics. Cambridge University Press.
2. Benjamin, T. B. 1961 The development of three-dimensional disturbances in an unstable film of liquid flowing down an inclined plane. J. Fluid Mech. 10, 401-419.
3. Bers, A. 1983 Space-time evolution of plasma instabilities - absolute and convective. In Handbook of plasma physics (ed. M. N. Rosenbluth & R. Z. Sagdeev), vol. 1, pp. 451-517. Amsterdam: North-Holland.
4. Brevdo, L. 1988 A study of absolute and convective instabilities with an application to the Eady model. Geophys. Astrophys. Fluid Dynam. 40, 1-92.
5. Brevdo, L. 1995 Convectively unstable wave packets in the Blasius boundary layer. Z. Angew. Math. Mech. 75, 423-436.
6. Brevdo, L. 2001 Neutral stability and resonant destabilization of the Earth's crust. Proc. R. Soc. Lond. A 457, 1951-1971.
7. Brevdo, L. 2002 A dynamical system approach to the absolute instability of spatially developing localized open flows and media. Proc. R. Soc. Lond. A 458, 1375-1397.
8. Brevdo, L. & Bridges, T. J. 1996 Absolute and convective instabilities of spatially periodic flows. Phil. Trans. R. Soc. Lond. A 354, 1027-1064.
9. Brevdo, L. & Bridges, T. J. 1997a Local and global instabilities of spatially developing flows: cautionary examples. Proc. R. Soc. Lond. A 453, 1345-1364.
10. Brevdo, L. & Bridges, T. J. 1997b Absolute and convective instabilities of temporally oscillating flows. Z. Angew. Math. Phys. 48, 290-309.
11. Brevdo, L., Laure, P., Dias, F. & Bridges, T. J. 1999 Linear pulse structure and signalling in a film flow on an inclined plane. J. Fluid Mech. 396, 37-71.
12. Briggs, R. J. 1964 Electron-stream interaction with plasmas. Cambridge, MA: MIT Press.
13. Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Math. 84, 119-144.
14. Drazin, P. G. & Johnson, R. S. 1989 Solitons: an introduction. Cambridge University Press.
15. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic stability. Cambridge University Press.
16. Eastham, M. S. P. 1989 The asymptotic solution of linear differential systems: applications of the Levinson theorem. Oxford: Clarendon.
17. Gaster, M. 1968 The development of three-dimensional wave packets in a boundary layer. J. Fluid Mech. 32, 173-184.
18. Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151-168.
19. Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. A. Rev. Fluid Mech. 22, 473-537.
20. Iooss, G. & Adelmeyer, M. 1992 Topics in bifurcation theory and applications. World Scientific.
21. Iooss, G. & Kirchgässner, K. 1992 Water waves for small surface tension: an approach via normal form. Proc. R. Soc. Edinb. A 122, 267-299.
22. Iooss, G. & Pérouème, M.-C. 1993 Perturbed homoclinic solutions in reversible 1:1 resonance vector fields. J. Diff. Eqns 102, 62-88.
23. Kato, T. 1980 Perturbation theory for linear operators. Springer.
24. Kirchgässner, K. 1988 Nonlinearly resonant surface waves and homoclinic bifurcation. Adv. Appl. Mech. 26, 135-181.
25. Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53-83.
26. Lang, S. 1965 Algebra. Addison-Wesley.
27. Le Dizès, S. 1997 Global modes in falling capillary jets. Eur. J. Mech. B 16, 761-778.
28. Le Dizès, S., Huerre, P., Chomaz, J.-M. & Monkewitz, P. A. 1996 Linear global modes in spatially developing media. Phil. Trans. R. Soc. Lond. A 354, 169-212.
29. Levinson, N. 1948 The asymptotic nature of solutions of linear systems of differential equations. Duke Math. J. 15, 111-126.
30. Lingwood, R. J. 1995 Absolute instability of the boundary layer on a rotating disk. J. Fluid Mech. 299, 17-33.
31. Mathis, C., Provansal, M. & Boyer, L. 1984 The Bénard-von Kármán instability: an experimental study near the threshold. J. Phys. Paris Lett. 45, 483-491.
32. Monkewitz, P. A., Bechert, D. W., Lehmann, B. & Barsikow, B. 1990 Self-excited oscillations and mixing in heated round jets. J. Fluid Mech. 213, 611-639.
33. Sandstede, B. 2002 Stability of traveling waves. In Handbook of dynamical systems II (ed. B. Fiedler), pp. 982-1055. Elsevier.
34. Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7, 309-317.
35. Strykowski, P. J. & Niccum, D. L. 1991 The stability of countercurrent mixing layers in circular jets. J. Fluid Mech. 227, 309-343.