DIFFUSIVE ESCAPE IN A NONLINEAR SHEAR-FLOW - LIFE AND DEATH AT THE EDGE OF A WINDY CLIFF

The survival probability of a particle diffusing in the two-dimensiona l domain x > 0 near a ''windy cliff'' at x = 0 is investigated. The pa rticle dies upon reaching the edge of the cliff. In addition to diffus ion, the particle is influenced by a steady ''wind shear'' with veloci ty v(x,y) = v sign (y)(X) over cap, i.e., no average bias either towar d or away from the cliff For this semi-infinite system, the particle s urvival probability decays with time as t(-1/4), compared to t(-1/2) i n the absence of wind. Scaling descriptions are developed to elucidate this behavior, as well as the survival probability within a semi-infi nite strip of finite width \y\ < w with particle absorption at x = 0. The behavior in the strip geometry can be described in terms of Taylor diffusion, an approach which accounts for the crossover to the t(-1/4 ) decay when the width of the strip diverges. Supporting numerical sim ulations of our analytical results are presented.