Escape Probability, Mean Residence Time and Geophysical Fluid Particle Dynamics

Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between flow regimes of different characteristic motion. We consider a quasigeostrophic meandering jet model with random perturbations. This jet is parameterized by the parameter $\beta = (2\Omega)/r \cos (\theta)$, where $\Omega$ is the rotation rate of the earth, $r$ the earth's radius and $\theta$ the latitude. Note that $\Omega$ and $r$ are fixed, so $\beta$ is a monotonic decreasing function of the latitude. The unperturbed jet (for $0 < \beta < 2/3$) consists of a basic flow with attached eddies. With random perturbations, there is fluid exchange between regimes of different characteristic motion. We quantify the exchange by escape probability and mean residence time.