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.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).

Enstrophy dynamics of stochastically forced large-scale geophysical flows

“…Notice also that the series in (16) is finite according to (5). Lemma 2 implies that (15) is satisfied for any t ≤ C/ϕ(α).…”

“…There has been active recent research on stochastic approaches to geophysical flows [19,18,14,24,4] and numerical simulations of stochastically forced geophysical flows [25,26,5,6,27]. It is generally understood that random fluctuations can have delicate impact on geophysical fluid dynamics [19,14,25,26,10].…”

Dynamical behavior of the activator–repressor circuit model under random fluctuations

“…This equation is solved via a finite element code [2,3]. The (spatial) average mean residence time U is defined by In particular, we consider a cellular domain which surrounds the fixed point, in order to investigate more detailed behavior about this stochastic system.…”

Discovering mean residence time and escape probability from data of stochastic dynamical systems

“…It is desirable to extract deterministic quantities that carry dynamical information of stochastic differential equations (SDEs). These deterministic quantities include moments a) Electronic mail: wudengfeng@mail.cncnc.edu.cn b) Electronic mail: mmfucaathy@163.com c) Electronic mail: duan@iit.edu for solution paths, probability density functions for solution paths, mean residence time and escape probability 7,9 . These concepts help us to understand various phenomena in complex systems under uncertainty 1 .…”