On passage through resonances in volume-preserving systems

Details On passage through resonances in volume-preserving systems On passage through resonances in volume-preserving systems

2006-04-20

arxiv.org/abs/nlin/0604047v1

Nonlinear Sciences

Chaotic Dynamics

23 pages and 9 Figures

Scientific paper

Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3-D volume-preserving slow-fast systems. We propose a general theory of those processes and apply it to a class of viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the phenomena during a single passage through resonance and show that multiple passages lead to the chaotic advection and mixing. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resulting mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances.

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