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TRANSITION TO CHAOS IN A SHELL MODEL OF TURBULENCE WITH THE CHANGE OF THE VISCOSITY.
- Source :
-
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics . 11/10/2011, Vol. 25 Issue 28, p3785-3795. 11p. - Publication Year :
- 2011
-
Abstract
- In this paper, a shell model for the energy cascade in three-dimensional turbulence at varying the viscosity is studied. When the viscosity parameter ν is large enough, the phase orbit of each shell in the system is a stable fixed point. As ν diminishes down to a critical value, the point becomes unstable and a stable periodic orbit appears via a supercritical Hopf bifurcation. For the quasiperiodic solution of the system, each shell has a own dynamic behavior. At ν = 6.88×10-5, the system initiates a complex scenario of bifurcations, where the phase orbits of un and un+3 begin to form a intersected section. Farther decreasing ν, we observe a transition from quasiperiodic solution to chaos through a sequence of Neimark-Sacker bifurcations. The behaviors can be vividly shown in the change of the average energy function E with ν. At last, the transition to chaos in the ν-δ parameter space is also obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02179792
- Volume :
- 25
- Issue :
- 28
- Database :
- Academic Search Index
- Journal :
- International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics
- Publication Type :
- Academic Journal
- Accession number :
- 67043725
- Full Text :
- https://doi.org/10.1142/S0217979211101715