Local models of spatio-temporally complex fields

Physica D: Nonlinear Phenomena

Volumn 90, Issue 4, 1996, Pages 387-407

  Dankowicz, Harry ^a   Holmes, Philip ^b   Berkooz, Gal ^c   Elezgaray, Juan ^d  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b Princeton University   (United States)

^c Cornell University   (United States)

^d CENTRE DE RECHERCHE PAUL PASCAL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000385041     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00245-6     Document Type: Article

References (18)

1. N. Aubry P. Holmes, J.L. Lumley and E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer, J. Fluid Mech. 192 (1988) 115-173.
2. G. Berkooz, P. Holmes and J.L. Lumley, Intermittent dynamics in simple models of the wall layer, J. Fluid Mech. 230 (1991) 75-95.
3. G. Berkooz, P. Holmes and J.L. Lumley, On the relation between low dimensional models and the dynamics of coherent structures in the turbulent wall layer, Theoret. Comput. Fluid Dynamics 4 (1993) 255-269.
4. G. Berkooz, P. Holmes and J.L. Lumley, The proper orthogonal decomposition in turbulent flows, Ann. Rev. Fluid Mech. 25 (1993) 539-575.
5. G. Berkooz, J. Elezgaray and P. Holmes, Coherent structures in random media and wavelets, Physica D 61 (1992) 47-58.
6. J. Jimenez and P. Moin, The minimal flow unit in near-wall turbulence, J. Fluid Mech. 225 (1991) 213-240.
7. J. Elezgaray, G. Berkooz and P. Holmes, Wavelet analysis of the motion of coherent structures, in: Progress in Wavelet Analysis and Applications, Y. Meyer and S. Roques, eds. (Editions Frontières, Gif-sur-Yvette, 1993).
8. M. Myers P. Holmes, J. Elezgaray and G. Berkooz, Wavelet projections of the Kuramoto-Sivashinsky equation I: heteroclinic cycles and modulated traveling waves for short systems, Physica D 86 (1995) 396-427.
9. G.I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames, part i: Derivation of the basic equations, Acta Astronautica 4 (1977) 1176-1206.
10. Y. Kuramoto, Diffusion-induced chaos in reaction systems, Suppl. Prog. Theor. Phys. 64 (1978) 346-367.
11. D. Armbruster, J. Guckenheimer and P. Holmes, Kuramoto-Sivashinsky dynamics on the center-unstable manifold, SIAM J. Appl. Math. 49 (1989) 676-691.
12. I.G. Kevrekidis, B. Nicolaenko and J. Scovel, Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math. 50 (1979) 760-790.
13. S. Toh, Statistical model with localized structures describing the spatio-temporal chaos of the Kuramoto-Sivashinsky equation, J. Phys. Soc. Jpn 56 (1987) 949-962.
14. D. Armbruster, J. Guckenheimer and P. Holmes, Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry, Physica D 29 (1988) 257-282.
15. A. Mielke, private communication.
16. G. Berkooz, Turbulence, Coherent Structures and Low Dimensional Models, Ph.D. Thesis, Cornell University (1991).
17. G. Berkooz and E. Titi, (1995), in preparation.
18. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, fourth corrected printing (Springer, New York, 1994).