1994/02/22 by Luca Biferale, A. Lambert, Biferale, L. +5
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed Matter (cond-mat) #Cosmology and Gravitation Theories #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.cond-mat/9402091
openalex publication_date 1994/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.