Rate of growth of the coalescent set in a coalescing stochastic flow

Consider an isotropic stochastic flow in R_d (i.e. a simultaneous random, correlated motion of all points in space), where d=l,2 or 3, such that the joint law of the motion of two particles allows the particles to meet and coalesce in finite time. The coalescent set J _t is a random subset of R_d consisting of the initial positions of particles which have coalesced by time t with the particle which started at 0. We show that the expected volume of J t grows at a rate proportional to when d=1, and at rates close to proportional to t/log t (resp. t) when d = 2 (resp. d=3). We give an example of a coalescing stochastic flow when d = 3. These results are analogous to growth rates of expected population size of a surviving type in the "invasion process" described by Clifford and Sudbury