The quasi-periodic doubling cascade in the transition to weak turbulence

Physica D: Nonlinear Phenomena

Volumn 210, Issue 3-4, 2005, Pages 249-261

  Van Veen, L ^a  

^a LA TROBE UNIVERSITY   (Australia)

Author keywords

Torus bifurcation; Transition to turbulence

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL FLUID DYNAMICS; INCOMPRESSIBLE FLOW; LYAPUNOV METHODS; RESONANCE; TURBULENT FLOW;

FREQUENCY SPECTRUM; QUASI-PERIODIC DOUBLING; TRANSITION TO TURBULENCE; TURBULENT BEHAVIOR;

NAVIER STOKES EQUATIONS;

EID: 25144520508     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.07.020     Document Type: Article

References (21)

1. M.E. Brachet, D.I. Meiron, S.A. Orszag, B.G. Nickel, R.H. Morf, and U. Frisch Small-scale structure of the Taylor-Green vortex J. Fluid Mech. 130 1983 411 452
2. S. Kida Three-dimensional periodic flows with high-symmetry J. Phys. Soc. Jpn. 54 1985 2132 2136
3. S. Kida, and Y. Murakami Statistics of velocity gradients in turbulence at moderate Reynolds number Fluid Dyn. Res. 4 1989 347 370
4. S. Kida, and Y. Murakami Kolmogorov similarity in freely decaying turbulence Phys. Fluids 30 1987 2030 2039
5. O.N. Boratav, and B.P. Pelz Structures and structure functions in the inertial range of turbulence Phys. Fluids 9 1997 1400 1415
6. K. Lust, D. Roose, A. Spence, and A.R. Champneys An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions SIAM J. Sci. Comput. 19 1998 1188 1209
7. J. Sánchez, M. Net, B. García-Archilla, and C. Simó Newton-Krylov continuation of periodic orbits for Navier-Stokes flows J. Comput. Phys. 201 2004 12 33
8. S. Kida, M. Yamada, and K. Ohkitani A route to chaos and turbulence Physica D 37 1989 116 125
9. K. Kaneko Collapse of Tori and Genesis of Chaos in Dissipative Systems 1986 World Scientific Singapore
10. A. Arnéodo, P.H. Coullet, and E.A. Spiegel Cascade of period doublings of tori Phys. Lett. A 94 1983 1 5
11. C. Simó, On the analytical and numerical approximation of invariant manifolds, in: Proceedings of the 13th Spring School on Astrophysics in Goutelas on Modern Methods in Celestial Mechanics, Edition Frontières, Gift-sur Yvette, France, 1989, Available via http://www.maia.ub.es/dsg/2004/index.html.
12. H.W. Broer, G.B. Huitema, and F. Takens Unfoldings of quasi-periodic tori Mem. AMS 83 421 1990 1 82
13. B.L.J. Braaksma, H.W. Broer, and G.B. Huitema Toward a quasi-periodic bifurcation theory Mem. AMS 83 421 1990 83 175
14. F. Schilder, H.M. Osinga, and W. Vogt Continuation of quasi-periodic invariant tori Applied Nonlinear Dynamics Preprint 2004 University of Bristol (2004.11)
15. V.S. Anishenko Complex Oscillations in Simple Systems 1990 Nauka Moscow
16. G.-Q. Zhong, W.W. Chai, and L.O. Chua Torus-doubling bifurcations in four mutually coupled Chua's circuits IEEE Trans. Circuits Syst. I 45 1998 186 193
17. V. Franceschini Bifurcation of tori and phase locking in a dissipative system of differential equations Physica D 6 1983 285 304
18. H.W. Broer, C. Simó, and R. Vitolo Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing Nonlinearity 15 2002 1205 1267
19. J.J. Stagliano, J.-M. Wersinger, and E.E. Slaminka Doubling bifurcations of destroyed T 2 tori Physica D 92 1996 164 177
20. G. Mayer-Kress, and H. Haken An explicit construction of a class of suspensions and autonomous differential equations for diffeomorphisms in the plane Commun. Math. Phys. 111 1987 63 74
21. M.J. Feigenbaum The transition to aperiodic behaviour in turbulent systems Commun. Math. Phys. 77 1980 65 86