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

摘要

We investigate a quasigeostrophic vortex flow with random perturbations. The system we will look at is rotating and has a gradient in the Coriolis force (the force due to the earth's rotation). When these two characteristics are present, the conserved quantity is the potential vorticity q=∇2ψ+βy. Thus, the dynamics are determined by the quasigeostrophic equation (∂t+v→·∇)q=0. In this, the parameter β is proportional to the Coriolis force gradient. Whenever 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 fluid domain, and the mean residence time of fluid particles inside a fluid domain. The goal of this paper is to determine the relationship between the parameter β and the escape probability and the mean residence time. We will look at a vortex of the flow and determine the escape probability crossing the upper and lower boundaries of the vortex of a particle (we assume that the particles are uniformly distributed in the vortex). We will also calculate the mean residence time for a particle inside a vortex. We find that as β increases, the escape probability for a particle crossing the lower boundary decreases. We also find that as β increases the mean residence time of a particle inside a vortex decreases.