Transition to Chaos in a Shell Model of Turbulence
| dc.creator | Biferale, L. | |
| dc.creator | Lambert, A. | |
| dc.creator | Lima, R. | |
| dc.creator | Paladin, G. | |
| dc.date | 1994-02-22 | |
| dc.date | 1994-02-23 | |
| dc.date.accessioned | 2026-07-07T08:58:49Z | |
| dc.date.available | 2026-07-07T08:58:49Z | |
| dc.description | We study a shell model for the energy cascade in three dimensional turbulence at varying the coefficients of the non-linear terms in such a way that the fundamental symmetries of Navier-Stokes are conserved. When a control parameter $ε$ related to the strength of backward energy transfer is enough small, the dynamical system has a stable fixed point corresponding to the Kolmogorov scaling. This point becomes unstable at $ε=0.3843...$ where a stable limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal decomposition, the transition to chaos is shown to follow the Ruelle-Takens scenario. For $ε> 0.3953..$ the dynamical evolution is intermittent with a positive Lyapunov exponent. In this regime, there exists a strange attractor which remains close to the Kolmogorov (now unstable) fixed point, and a local scaling invariance which can be described via a intermittent one-dimensional map. | |
| dc.description | 16 pages, Tex, 20 figures available upon request to the authors | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9402091 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9402091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147474 | |
| dc.subject | Condensed Matter | |
| dc.title | Transition to Chaos in a Shell Model of Turbulence | |
| dc.type | text |