Mathematical Problems in Engineering
Volume 7 (2001), Issue 1, Pages 55-65

Escape probability and mean residence time in random flows with unsteady drift

James R. Brannan,1 Jinqiao Duan,2 and Vincent J. Ervin1

1Department of Mathematical Sciences, Clemson University, Clemson 29634, South Carolina, USA
2Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, IL, USA

Received 1 September 1999; Revised 28 July 2000

Copyright © 2001 James R. Brannan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.