It is far easier to follow a stick floating on a slowly moving stream than to trace a bottle bobbing in an angry sea. Being full of random movements with unexpected turns and uneven displacements, the path of the bottle is almost certainly what a physicist would call chaotic. While it seems unlikely, might the floating stick also show such path chaos? In a newly published work, appearing in the journal Physical Review Letters, Shi-Yuan Hu and his colleagues reveal that it is indeed possible, especially if the stick, or structure as the authors call it, has a size comparable to the eddies of the slow-moving flows. Their study also shows, besides the path chaos, the floating stick can be trapped in an eddy, wander aimlessly, or move along a straight line with zigzag steps.
"All these behaviors depend on the structure's size and rigidity. And it is surprising to see chaos arises from a low Reynolds number system like ours," says Dr. Jun Zhang, a professor of Physics and Mathematics of NYU Shanghai and NYU, citing that "The Reynolds number is a measure on how active a fluid-structure system can be, roughly speaking."
The system under study is an array of small rotating flow eddies, through which a flexible structure is carried by the flow. The team of researchers focused on how structures of different lengths and rigidities, move about over very long times.
"The background flow is trivial, being slow and steady, but once the elongated structure is placed in it, the interaction between the structure and the flow becomes interesting and unexpected. It's almost like a billiard ball being softly bounced back and forth by the flow's eddies," says Professor Michael Shelley, a math professor based at NYU and the Flatiron Institute.
This research combines numerical simulations and experimental observations. The experiments were conducted in the joint physics laboratory located in the NYU-ECNU Institute of Physics at NYU Shanghai. The lead author is a rising 5th year Ph.D. student Shi-Yuan Hu, followed by a 2nd-year visiting student from Tongji University, Jun-Jun Chu.
"Since structures of different lengths behave differently," Hu and Zhang further comment, "Our findings may be used someday in the sorting of biopolymers such as large DNA molecules."
A semi-flexible filament interacts with an array of spinning flow eddies. Depending on its length and rigidity, the filament could undergo chaotic motion, or move along straight lines, and even become trapped. Image copyright to the first author Shi-Yuan Hu.