# Probability of noise-induced separatrix crossing for inertial particles in flows

## TL;DR

This paper derives an analytical expression for the probability that weakly inertial particles in steady 2D flows will cross flow separatrices due to noise, enabling prediction without solving detailed trajectories.

## Contribution

It introduces a novel asymptotic method to analytically compute noise-induced separatrix crossing probabilities for inertial particles in steady flows.

## Key findings

- Analytical expression for crossing probability derived
- Method applicable to various steady 2D flows
- Does not require solving particle trajectories

## Abstract

The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles to enter or exit recirculation cells in an unpredictable manner. An analytical expression for the probability of separatrix crossing is obtained. It can be applied to a wide variety of flows, provided some elementary kinematical quantities of the fluid flow are known. It does not require to solve particle trajectories.