The effect of changing the Coriolis force gradient parameter on the escapeprobability and mean residence time

We investigate a quasigeostrophic vortex flow with random perturbations. Th e system we will look at is rotating and has a gradient in the Coriolis for ce (the force due to the earth's rotation). When these two characteristics are present, the conserved quantity is the potential vorticity q = del (2)p si + beta gamma. Thus, the dynamics are determined by the quasigeostrophic equation (partial derivative (t) + (v) over right arrow . del )q = 0. In th is, the parameter beta is proportional to the Coriolis force gradient. When ever we have a system with random perturbations, we may talk of the escape probability of fluid particles crossing a portion of the boundary for a flu id domain, and the mean residence time of fluid particles inside a fluid do main. The goal of this paper is to determine the relationship between the p arameter beta and the escape probability and the mean residence time. We wi ll look at a vortex of the flow and determine the escape probability crossi ng the upper and lower boundaries of the vortex of a particle (we assume th at the particles are uniformly distributed in the vortex). We will also cal culate the mean residence time for a particle inside a vortex. We find that as beta increases, the escape probability for a particle crossing the lowe r boundary decreases. We also find that as beta increases the mean residenc e time of a particle inside a vortex decreases. (C) 2001 Elsevier Science I nc. All rights reserved.