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Resonant chaotic mixing in a cellular flow

This paper presents a quantitative theory of resonant mixing in time-dependent volume-preserving $3D$ flows using a model cellular flow introduced in [T. Solomon and I. Mezic, Nature, 425, 376 (2003) as an example.

Specifically, we show that chaotic advection is dramatically
enhanced by a time-dependent perturbation for certain resonant frequencies. We compute the fraction of the mixed volume as a function of the frequency of the
perturbation and show that essentially complete mixing in 3D is achieved at every resonant frequency.
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