Braiding Patterns in Flowing Streams

Braiding patterns in flowing streams have been explained by a University of New Mexico team (Vakhtang Putkaradze, 505-277-2234, putkarad@math.unm.edu).

Attention poets: researchers have figured out the secrets behind a beautiful fluid pattern that sharp-eyed observers can occasionally witness in thin, narrow streams of water flowing down a hill.

Ordinarily, a stream of water meanders, or goes side to side, when it flows down an inclined plane that is "partially wetting," or not perfectly water-repelling. Some researchers considered such meandering to be inevitable, even for water flowing down a perfectly smooth plane.

But the New Mexico team discovered, first of all, that meandering can be eliminated (the centerline of the stream can be straight) if water flows down the plane at a constant rate, a somewhat rare but possible occurrence. Moreover, such non-meandering streams often have visually striking "braids," a fixed pattern of wide and narrow water regions that goes all the way down the plane.

Using a simple laboratory setup, the researchers discovered an easy way to duplicate this braiding pattern (see Physics News Graphics). They sent a fluid (a mix of water, glycerol and some food coloring) down a narrow cylindrical nozzle. As it exited the nozzle the fluid struck a slanted acrylic plane, where it formed a braiding pattern as it ran downstream into a lower reservoir.

Describing the lab fluid's behavior with equations, the researchers found that braiding occurs as a competition between the fluid's inertia and surface tension: As the fluid strikes the acrylic plane, it tends to keep moving, causing it to spread out. However, surface tension limits the spreading and quickly manages to pull the fluid back together to a narrow waist. Nonetheless, in the process of forming this waist, the outer edges (which carry most of the fluid) "bounce" on impact and push the fluid apart. This process repeats to create several braids.

The researchers found it easy to tweak the braid's properties; for example, they could decrease the length of the braids by making the plane less steep and they could eliminate the braids altogether by increasing the viscosity of the fluid. It is possible these observations have geophysical implications, but more research is needed to say that with certainty. (K. Mertens, V. Putkaradze, and P. Vorobieff, Nature, 8 July 2004.)