Recovering coefficients of the complex Ginzburg-Landau equation from experimental spatio-temporal data: Two examples from hydrodynamics

Physica D: Nonlinear Phenomena

Volumn 174, Issue 1-4, 2003, Pages 114-133

  Le Gal, P ^a   Ravoux, J F ^a   Floriani, E ^b   De Wit, T Dudok ^c  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b CNRS   (France)

^c LPCE CNRS   (France)

Author keywords

Ginzburg Landau equation; Proper orthogonal decomposition; Spatio temporal chaos; Volterra expansion

Indexed keywords

CHAOS THEORY; DECOMPOSITION; ROTATING DISKS; WAVE EQUATIONS;

SPATIO-TEMPORAL CHAOS;

HYDRODYNAMICS;

EID: 0037212146     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00686-3     Document Type: Conference Paper

References (33)

1. O. Nelles, Nonlinear System Identification, Springer, Berlin, 2001.
2. Zdravkovich M., Review of flow interference between two circular cylinders in various arrangements. Trans. ASME, J. Fluids Eng. 99:1977;618.
3. Chang K.S., Song C.J., Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement. Int. J. Numer. Meth. Fl. 11:1990;317.
4. Peschard I., Le Gal P., Coupled wakes of cylinders. Phys. Rev. Lett. 77:1996;3122.
5. Le Gal P., Chaos spatio-temporel dans une chaîne de sillages couplés. C R. Acad. Sci. 313(II):1991;1499.
6. M. Provansal, C. Mathis, L. Boyer, Bénard-Von Karman instability: transient and forced regimes, J. Fluid Mech. 182 (1987).
7. Dusek J., Le Gal P., Fraunié Ph., A numerical and theoretical study of the first bifurcation in a cylinder wake. J. Fluid Mech. 264:1994;172.
8. Cardoso O., Willaime H., Tabeling P., Short-wavelength instability in a linear array of vortices. Phys. Rev. Lett. 65:1990;1869.
9. W. Eckhaus, Studies in Nonlinear Stability Theory, Springer, Berlin, 1965.
10. A.C. Newell, Envelope equations, Lect. Appl. Math. 15 (1974).
11. Matkowsky B.J., Volpert V., Stability of plane wave solutions of complex Ginzburg-Landau equations. Quart. Appl. Math. 51(2):1993;265.
12. Willaime H., Cardoso O., Tabeling P., Coupled oscillators: an accurate model for describing the dynamics of lines of vortices. Eur. J. Mech. B. 10(2):1991;165.
13. Ravoux J.F., Le Dizes S., Le Gal P., Stability analysis of plane wave solutions of the discrete Ginzburg-Landau equation. Phys. Rev. E. 61:2000;390.
14. Croquette V., Williams H., Nonlinear waves of the oscillatory instability of finite convective rolls. Physica D. 37:1989;300.
15. Ravoux J.F., Le Gal P., Bi-orthogonal decomposition analysis and reconstruction of spatio-temporal chaos generated by coupled wakes. Phys. Rev. E. 58:1998;R5233.
16. Fullana J.M., Le Gal P., Rossi M., Zaleski S., Identification of parameters in an amplitude equation describing coupled wakes. Physica D. 102:1999;35.
17. Vallette D.P., Jacobs G., Gollub J.P., Oscillations and spatio-temporal chaos of one-dimensional fluid fronts. Phys. Rev. E. 55:1997;4274.
18. Voss H.U., Kolodner P., Abel M., Kurths J., Amplitude equations from spatiotemporal binary-fluid convection data. Phys. Rev. Lett. 83:1999;3422.
19. Bär M., Hegger R., Kantz H., Fitting partial differential equations to space-time dynamics. Phys. Rev. E. 59:1999;337.
20. P. Holmes, J.L. Lumley, G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, 1996.
21. Chauve M.P., Le Gal P., Complex bi-orthogonal decomposition of a chain of coupled wakes. Physica D. 58:1992;407.
22. Aubry N., Guyonnet R., Lima R., Spatio-temporal analysis of complex signals: theory and applications. J. Stat. Phys. 64:1991;683.
23. Ekman V.W., On the influence of the earth's rotation on ocean currents. Arkiv. Mat. Astr. Fys. 2(11):1905;1.
24. Von Karman T., Über laminare und turbulente Reibung. Z. Angew. Math. Mech. 1:1921;233.
25. Gregory N., Stuart J.T., Walker W.S., On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A. 248:1955;155.
26. Jarre S., Le Gal P., Chauve M.P., Experimental study of rotating disk flow instability. I. Natural flow. Phys. Fluids. 8:1996;496.
27. Jarre S., Le Gal P., Chauve M.P., Experimental study of rotating disk flow instability. II. Forced flow. Phys. Fluids. 8:1996;2985.
28. Floriani E., Dudok de Wit T., Le Gal P., Nonlinear interactions in a rotating disk flow: from a Volterra model to the Ginzburg-Landau equation. Chaos. 10(4):2000;834.
29. M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, Wiley, Chichester, NY, 1980.
30. Billings S.A., Identification of nonlinear systems - a survey. Proc. IEE D. 127:1980;272.
31. Moon H.T., Huerre P., Redekopp L.G., Transitions to chaos in the Ginzburg-Landau equation. Physica D. 7:1983;135.
32. Le Gal P., Complex demodulation applied to the transition to turbulence of the flow over a rotating disk. Phys. Fluids A. 4(11):1992;2523.
33. Lingwood R.J., Absolute instability of the Ekman layer and related rotating flows. J. Fluid Mech. 314:1995;373.