Flapping flags may shed light on how fish school and birds flock
OFTEN it pays not to be leader of the pack—just ask a racing cyclist or a Formula One driver. Conserving energy by following the leader, a trick known as slipstreaming, can give a rider or driver that extra bit of juice to pull ahead at the very last moment. In the natural world, however, bodies are more likely to be flexible, like a fish’s, rather than rigid, like a car’s. In these systems, as a recent paper in Physical Review Letters reports, it is the leader that enjoys a significant dynamic advantage over the followers.
Jun Zhang of New York University came to this conclusion obliquely, by examining one of life’s burning questions: why is it that flags flutter in a breeze? Flags are good analogues of birds and fish because all three change their shape as they move through a fluid. In 2000 Dr Zhang did some experiments to study the motion of thin silk filaments (standing in for flags) in flowing films of liquid dishwashing soap (standing in for the breeze).
As the soap film “blew” past a flag it formed streams and eddies. Dr Zhang was able to observe these by illuminating it. Light bouncing within the film between its surfaces creates an interference pattern (this is why soap bubbles appear coloured). Streams and eddies in such a film alter its thickness, and thus the details of this interference pattern, allowing the pattern of irregularities induced by the flag to be captured on camera.
These initial experiments revealed that fluttering is an intrinsic feature of the motion of a flag. Make a flag long enough, and it will flutter no matter how steady the breeze. This is because the shape of the flag changes. Any small instability in shape causes changes in the flow of fluid, which alters the shape further. The whole process thus amplifies the fluttering.
Now, in collaboration with Leif Ristroph of Cornell University, Dr Zhang has used the same technique to look at what happens when there are several objects in the moving fluid—a series of flags outside a government office, for example, or a line of fish in a school.
In this case, the researchers were surprised to find that the familiar physics of slipstreaming were inverted. If one flag has a second downwind of it, that second breaks up the wake of the leader. This stops that wake being a single, coherent back-and-forth wave. As a result, the leading flag flies straighter. In a line of many flags, moreover, most experience this reduced drag in turn, making the whole group more aero- (or hydro-) dynamic.
Inverted slipstreaming of this sort could have some counterintuitive effects. A fish frantically trying to escape from a predator might get the advantage of reduced drag. As the team put it in their paper, “it is better to be chased than to chase.” However, fish and birds actively change their shape when they swim and fly, whereas flags flutter passively in the breeze. Whether this makes a difference is not yet clear. The researchers therefore plan follow-up tests with aquarium fish to see if they, too, experience inverted slipstreaming. If they do, then there may, eventually, be engineering applications. Whether wobbly bikes and flexible racing cars are among them remains to be seen.