Suppose there are a finite number of disjoint unit-radii disks in the
plane, each spinning clockwise or counterclockwise at the same
The plane is filled with a thin fluid layer,
and the disks can be viewed as spinning fan blades
determining vectors of fluid motion tangent to the disks.
Is the resulting flow and vector field throughout the plane known?
My initial intuition is that there should be something like a
Voronoi diagram demarcating boundaries of regions of influence.
But in exploring a bit I find it may even be nontrivial to
determine the flow between just two counter-rotating vortices.
For example, the following image was
computed by Paul Nylander
based on a paper by
O.S. Kerr and J.W. Dold,
"Periodic Steady Vortices in a Stagnation Point Flow,"
J. Fluid Mech., 276, 307-325 (1994).
As I am quite unschooled in this topic, pointers to relevant literature might suffice. Thanks!
Edit1. I've now asked a revised version of this question on Math Overflow, incorporating the clarifying suggestions of Rahul. I might hit a fluid dynamics expert there.
Edit2. Thanks to Rahul and David Bar Moshe here, and Willie Wong and Bob Terrell on MO, I have a much broader understanding of the problem, and could likely compute a numerical solution if needed. I appreciate the help!