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Understanding the macroscopic behavior of dynamical systems is an importanttool to unravel transport mechanisms in complex flows. A decomposition of thestate space into coherent sets is a popular way to reveal this essentialmacroscopic evolution. To compute coherent sets from an aperiodictime-dependent dynamical system we consider the relevant transfer operators andtheir infinitesimal generators on an augmented space-time manifold. Thisspace-time generator approach avoids trajectory integration, and creates aconvenient linearization of the aperiodic evolution. This linearization can befurther exploited to create a simple and effective spectral optimizationmethodology for diminishing or enhancing coherence. We obtain explicitsolutions for these optimization problems using Lagrange multipliers andillustrate this technique by increasing and decreasing mixing of spatialregions through small velocity field perturbations.

Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration