The spreading and diffusion of two-dimensional vortices subject to weak, external, random strain fields is
examined. The response to such a field of given angular frequency depends on the profile of the vortex and can
be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used
to evolve the profile over a long time scale, using a diffusion equation that is both nonlinear and non-local.
This equation, containing an additional smoothing parameter, is simulated starting with a Gaussian vortex. The
evolution shows the development of vorticity steps, which are also studied using the the asymptotic model of
Balmforth, Llewellyn Smith and Young (J. Fluid Mech. 426, 95-133, 2001).