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 $β= (2Ω)/r \cos (θ)$, where $Ω$ is the rotation rate of the earth, $r$ the earth's radius and $θ$ the latitude. Note that $Ω$ and $r$ are fixed, so $β$ is a monotonic decreasing function of the latitude. The unperturbed jet (for $0 < β< 2/3$) 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.