Chaos and the Flow Capture Problem: Polluting is Easy, Cleaning is Hard

Abstract: Cleaning pollution from a heterogeneous flow environment is far from simple. We consider the flow capture problem, which has flows and sinks in a heterogeneous environment, and investigate the problem of positioning pollutant capture units. We show that arrays of capture units carry a high risk of failure without accounting for environmental heterogeneity and chaos in their placement, design, and operation. Our idealized 2-dimensional models reveal salient features of the problem. Maximum capture efficiency depends on the required capture rate: long term efficiency decreases as the number of capture units increases, whereas short term efficiency increases. If efficiency is important, the capture process should begin as early as feasible. Knowledge of transport controlling flow structures offers predictability for unit placement. We demonstrate two heuristic approaches to near-optimally position capture units.