Survival probability in a random velocity field

The time dependence of the survival probability S(t) is determined for diffusing particles in two dimensions which are also driven by a random unidirectional zero-mean velocity field vx(y). For a semi-infinite system with unbounded y and x.0, and with particle absorption at x50, a qualitative argument is presented which indicates that S(t);t. This prediction is supported by numerical simulations. A heuristic argument is also given which suggests that the longitudinal probability distribution of the surviving particles has the scaling form P(x ,t);tug(u). Here the scaling variable u}x/t, so that the overall time dependence of P(x ,t) is proportional to t, and the scaling function g(u) has the limiting dependences g(u)}const as u→0, and g(u);exp(2u) as u→` . This argument also suggests an effective continuum equation of motion for the infinite system which reproduces the correct asymptotic longitudinal probability distribution. @S1063-651X~97!01911-9#