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. For an eddy, the average escape probability for fluid particles (initially inside the eddy) escape into the exterior retrograde region is smaller than escape into the jet core for 0 < β < 0.3333, while for 0.3333 < β < 2 3 , the opposite holds. For a unit jet core near the jet troughs, the average escape probability for fluid particles (initially inside the jet core) escape into the northern recirculating region is greater than escape into the southern recirculating region for 0 < β < 0.115, while for 0.385 < β < 2 3 , the opposite holds. Moreover, for 0.115 < β < 0.385, fluid particles are about equally likely to escape into either recirculating regions. Furthermore, for a unit jet core near the jet crests, the situation is the opposite as for near the jet troughs. The maximal mean residence time of fluid particles initially in an eddy increases as β increases from 0 to 0.432 (or as latitude decreases accordingly), then decreases as β increases from 0.432 to 2 3 (or as latitude decreases accordingly). However, the maximal mean residence time of fluid particles initially in a unit jet core always increases as β increases (or as latitude decreases).