To better understand and optimize the capture of passive scalars (particles, pollutants, greenhouse gases, etc.) in complex geophysical flows, we study capture in the simpler, but still chaotic, time-dependent double-gyre flow model. For a range of model parameters, the domain of the double-gyre flow consists of a chaotic region, characterized by rapid mixing, interspersed with nonmixing islands in which particle trajectories are regular. Capture units placed within the domain remove all particles that cross their perimeters without altering the velocity field. To predict the capture capability of a unit at an arbitrary location, we characterize the trajectories of a uniformly seeded ensemble of particles as chaotic or nonchaotic, and then use them to determine the spatially resolved fraction of time that the flow is chaotic. With this information, we can predict where to best place units for maximum capture. We also examine the time dependence of the capture process, and demonstrate that there can be a trade-off between the amount of material captured and the capture rate.

• Received 4 June 2021
• Accepted 8 November 2021

DOI:https://doi.org/10.1103/PhysRevE.104.064203