Transport in Transitory, Three-Dimensional, Liouville Flows

Details Transport in Transitory, Three-Dimensional, Liouville Flows Transport in Transitory, Three-Dimensional, Liouville Flows

2012-03-16

arxiv.org/abs/1203.3821v1

Mathematics

Dynamical Systems

30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sys

Scientific paper

We derive an action-flux formula to compute the volumes of lobes quantifying transport between past- and future-invariant Lagrangian coherent structures of n-dimensional, transitory, globally Liouville flows. A transitory system is one that is nonautonomous only on a compact time interval. This method requires relatively little Lagrangian information about the codimension-one surfaces bounding the lobes, relying only on the generalized actions of loops on the lobe boundaries. These are easily computed since the vector fields are autonomous before and after the time-dependent transition. Two examples in three-dimensions are studied: a transitory ABC flow and a model of a microdroplet moving through a microfluidic channel mixer. In both cases the action-flux computations of transport are compared to those obtained using Monte Carlo methods.

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