Exit times of a Brownian particle out of a convection roll

We numerically investigated the transient dynamics of a passive colloidal particle in a periodic array of planar counter-rotating convection rolls at high Peclet numbers. We discovered that the distributions of first-exit times out of a single convection roll exhibit distinct regimes: an exponential tail, due to the noise-assisted diffusion of the trapped particle from the center toward the edge of the roll, and a peak structure emerging from a power-law background, associated with the transverse and longitudinal Brownian diffusion of the particle within the rolls' flow boundary layers. These results are interpreted analytically and related to the earlier literature on the topic.