Journal of Statistical Physics, Vol. 78, Nos. 1/2, 1995. p. 377-387.
The motion of a particle in two dimensions in a fluid is considered. The fluid flow is given and time independent. The complex fluid velocity potential can be viewed as a conformal transformation and after rescaling the time, the motion of the particle is uniform and rectilinear in the absence of diffusion. When diffusion of the particle also takes place the same ideas lead to a useful self-consistent approximation based on the average motion of the particle.