Local depletion of microswimmers in fluid flows due to rotational diffusion and tumbling

Microswimmer trajectories in externally-driven fluid flows are constrained by one-way transport barriers, obtained from certain invariant manifolds of the microswimmer equations of motion. Here, we theoretically investigate the effect of stochastic swimmer reorientation in the presence of these one-way barriers. We consider both rotational diffusion and tumbling, i.e. sudden jumps in the swimmer orientation. In both cases, we find that noise significantly increases the probability that swimmers cross these one-way barriers. This strongly constrains their subsequent trajectories and leads to a depletion of the density of swimmers near these barriers. For the two-dimensional linear hyperbolic flow, we quantify this depletion effect by calculating the probability of stochastic swimmer trajectories crossing these one-way barriers.