Escape probability, mean residence time and geophysical fluid particle dynamics

Stochastic dynamical systems arise as models for fluid particle motion in g eophysical hows with random velocity fields. Escape probability (from a flu id domain) and mean residence time tin a fluid domain) quantify fluid trans port 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 Omeg a is the rotation rate of the earth, r the earth's radius and theta the lat itude. Note that Omega and r are fixed, so beta is a monotonic decreasing f unction of the latitude. The unperturbed jet (for 0 ( beta < 2/3) consists of a basic flow with attached eddies. With random perturbations, there is f luid exchange between regimes of different characteristic motion. We quanti fy the exchange by escape probability and mean residence time. For an eddy, the average escape probability for fluid particles (initially inside the e ddy) escape into the exterior retrograde region is smaller than escape into the jet core for 0 < beta < 0.3333, while for 0.3333 < beta < 2/3, the opp osite holds. For a unit jet core near the jet troughs, the average escape p robability 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 < beta < 0.115, while for 0.385 < beta < 2/3, th e opposite holds. Moreover, for 0.115 < beta < 0.385, fluid particles are a bout equally likely to escape into either recirculating regions. Furthermor e, for a unit jet core near the jet crests, the situation is the opposite a s for near the jet troughs. The maximal mean residence time of fluid partic les initially in an eddy increases as beta increases from 0 to 0.432 (or as latitude decreases accordingly), then decreases as beta increases from 0.4 32 to 2/3 (or as latitude decreases accordingly). However, the maximal mean residence time of fluid particles initially in a unit jet core always incr eases as beta increases (or as latitude decreases). (C) 1999 Elsevier Scien ce B.V. All rights reserved.