1 research outputs found
Transition to Chaos in a Shell Model of Turbulence
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
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 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 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.Comment: 16 pages, Tex, 20 figures available as hard cop