Resonant mixing in perturbed action-action-angle flow.
This paper presents a quantitative theory of mixing via chaotic advection in near-integrable time-dependent volume-preserving flows for the case when the base (unperturbed) flow possesses two invariants (or actions). Using a model cellular flow introduced by Solomon and Mezic as an example, we construct a quantitative theory of mixing caused by the resonance-induced diffusion of an adiabatic invariant of the flow. We compute the fraction of the mixed volume as a function of the frequency of the perturbation and show that this function is strikingly nonmonotonic, with multiple peaks. In particular, essentially complete mixing inside a flow cell is achieved on experimentally accessible time scales for certain special frequencies.
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Dmitri L
DL
Vainchtein
John
J
Widloski
Roman O
RO
Grigoriev