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Suppose there are a finite number of disjoint unit-radii disks in the plane, each spinning clockwise or counterclockwise at the same angular velocity. 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 steady-state flow and vector field throughout the plane known? I asked a preliminary version of this question on Math SE, and received useful clarifications from user Rahul, who suggested starting with the assumptions that the fluid is incompressible, inviscid, and that the flow is irrotational.

My initial intuition is that there should be something like a Voronoi diagram demarcating boundaries of regions of influence. But my preliminary investigations suggest that 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!

Edit. Thanks to Willie Wong and Bob Terrell here, and Rahul and David Bar Moshe on MathSE, I have a much broader understanding of the problem, and could likely compute a numerical solution if needed. I appreciate the help!

3 added 13 characters in body

Suppose there are a finite number of disjoint unit-radii disks in the plane, each spinning clockwise or counterclockwise at the same angular velocity. 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 steady-state flow and vector field throughout the plane known? I asked a preliminary version of this question on Math SE, and received useful clarifications from user Rahul, who suggested starting with the assumptions that the fluid is incompressible, inviscid, and that the flow is irrotational.

My initial intuition is that there should be something like a Voronoi diagram demarcating boundaries of regions of influence. But my preliminary investigations suggest that 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!

2 added 1 characters in body

Suppose there are a finite number of disjoint unit-radii disks in the plane, each spinning clockwise or counterclockwise at the same angular velocity. 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? I asked a preliminary version of this question on Math SE, and received useful clarifications from user Rahul, who suggested starting with the assumption assumptions that the fluid is incompressible, inviscid, and that the flow is irrotational.

My initial intuition is that there should be something like a Voronoi diagram demarcating boundaries of regions of influence. But my preliminary investigations suggest that 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!

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