title: On passage through resonances in volume-preserving systems.
abstract: Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3D volume-preserving multiscale systems. We propose a general theory of those processes and apply it to a class of kinematic models inspired by 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 resultant mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances.
authors.affiliation: School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
authors.forename: D L
authors.initials: DL
authors.lastname: Vainchtein
authors.forename: A I
authors.initials: AI
authors.lastname: Neishtadt
authors.forename: I
authors.initials: I
authors.lastname: Mezic