Creating chaotic advection is the most efficient strategy to achieve mixing on microscale or in very viscous fluids. In this paper, we present a quantitative theory of the long-time resonant mixing in 3D near-integrable flows. We use the flow between two coaxial elliptic counter-rotating cylinders as a demonstrative model, where multiple scatterings on resonance result in mixing by causing the jumps of adiabatic invariants. We improve the existing estimates of the width of the mixing domain. We show that the resulting mixing both on short and long time scales can be described in terms of a single diffusion-type equation with a diffusion coefficient depending on the averaged effect of multiple passages through resonances. We discuss the exact location of the boundaries of the chaotic domain and show how it affects the properties of mixing.
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Resonance phenomena and long-term chaotic advection in volume-preserving systems
Vainchtein, Dmitri L.; Abudu, Alimu
Follow Chaos: An Interdisciplinary Journal of Nonlinear Science
, Volume 22 (1)
American Institute of Physics – Mar 1, 2012
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