Edge of Chaos and Genesis of Turbulence
Abraham C.-L. Chian, Pablo R. Mu\~noz, Erico Rempel
TL;DR
This paper investigates the transition to turbulence in a spatially extended system, revealing how chaotic saddles and edge states evolve through fractal metamorphoses leading to turbulence.
Contribution
It identifies the edge state as an unstable travelling wave and describes the smooth-fractal metamorphosis at the basin boundary in the context of turbulence onset.
Findings
Chaotic saddle emerges at the basin boundary due to smooth-fractal metamorphosis.
Transient turbulence develops via a cascade of fractal-fractal metamorphoses.
Unstable travelling wave acts as the edge state for chaos and turbulence genesis.
Abstract
The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable travelling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space.
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