The flow studied here is that due to a diffusing point vortex of
strength . We will normalize this problem by means
of
and an arbitrary characteristic length
. We take the Reynolds number of the flow correspondingly
as
. Thus normalized, the problem
is governed by the nondimensional vorticity equation
The initial condition is
The velocity follows from the Biot-Savart law [14],
or equivalently from the stream function :
Note that the problem is independent of the length scale , since the Reynolds number is. The only relevant length scale is the computational vortex spacing as compared to the diffusion distance . Our computation will therefore proceed from initial stages with no numerical resolution at all to later stages of increasing resolution. Despite the lack of resolution in the early stages, our computation turns out to be accurate (see section 9.1 for related theoretical results).