Going with the flow: enhancing stochastic switching rates in multi-gyre systems

TL;DR

This paper introduces a control strategy that leverages stochastic fluctuations in a double-gyre flow model to manipulate escape times between regions, demonstrating how noise can be used advantageously in fluid flow control.

Contribution

The paper presents a novel control approach that uses large fluctuation theory to manipulate stochastic escape times in multi-gyre systems, combining simulations and numerical methods.

Findings

Control can exponentially alter escape times between gyres.

Stochastic fluctuations can be harnessed to improve flow control.

Numerical simulations validate theoretical predictions.

Abstract

A control strategy is employed that modifies the stochastic escape times from one basin of attraction to another in a model of a double-gyre flow. The system studied captures the behavior of a large class of fluid flows that circulate and have multiple almost invariant sets. In the presence of noise, a particle in one gyre may randomly switch to an adjacent gyre due to a rare large fluctuation. We show that large fluctuation theory may be applied for controlling autonomous agents in a stochastic environment, in fact leveraging the stochastic- ity to the advantage of switching between regions of interest and concluding that patterns may be broken or held over time as the result of noise. We demonstrate that a controller can effectively manipulate the probability of a large fluctuation, thereby modifying escape times exponentially; this demonstrates the potential of optimal control strategies that work in combination with the endemic stochastic environment. To demonstrate this, stochastic simulations and numerical continuation are employed to tie together experimental findings with predictions.