Role of vortex organization in low-Reynolds-number mixing

Determine whether the similarity in vortex organization, rather than the detailed vortex geometry, is the primary reason for the similar mixing dynamics observed at Reynolds numbers satisfying Re less than or approximately equal to O(1).

Background

The paper compares laminar stirring at very low and order-one Reynolds numbers. In both cases, two vortices remain attached to the moving cylindrical stirrer, and the dye evolves toward a self-similar spiral pattern with mixing dominated by diffusion. Although the size and shape of the vortices differ between the cases, their locations relative to the stirrer’s circular path are similar.

The authors explicitly formulate a hypothesis that this similarity in vortex organization, rather than the detailed geometry of the vortices, explains the comparable mixing dynamics. The paper does not establish this causal relationship, leaving it as an unresolved question.