Escape Probability, Mean Residence Time and Geophysical Fluid Particle Dynamics

Abstract

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.