How do birds flock together?Researchers reveal previously unknown aerodynamic phenomenon through mathematical calculations

Look up at the sky during the first few weeks of spring and you’ll likely see a flock of birds moving in unison as they migrate north. But how do these creatures fly in such a coordinated and seemingly effortless way?

Part of the answer lies in precise, previously unknown aerodynamic interactions, a team of mathematicians reports in a newly published study. Its breakthrough broadens our understanding of wildlife, including fish, as they move in schools, and could have applications in transportation and energy.

“Research in this area is important because animals are known to take advantage of movements such as air or water left behind by other members of the group to save energy required to move or to reduce drag or drag,” explains Leif. Rirstrop, NYU Library Lang Institute of Mathematical Sciences associate professor and senior author of the paper, which appears in the journal nature communications.

“Our work may also have applications in transportation (such as efficient propulsion through air or water) and energy (such as more efficient harvesting of energy from wind, currents or waves).”

The team’s results show that the aerodynamic impact depends on the size of the flying group – favoring small groups as well as large groups.

“Aerodynamic interactions in small flocks help each member maintain a certain special position relative to its leading neighbor, but larger flocks are disturbed by an effect that displaces members from these positions. move away and could lead to a collision,” points out Sophie Ramananarivo, assistant professor at Ecole Polytechnique and one of the paper’s authors.

Previously, Listrov and his colleagues discovered how birds move in groups, but these findings were made through experiments that simulated the interaction of “two” birds.new nature communications The study expanded its investigation to identify many flyers.

To replicate the columnar structure of birds, researchers created mechanized flapping wings that act like bird wings. The wings are 3D printed from plastic and are driven by motors to flap in the water, replicating the flow of air around a bird’s wings during flight.

This “simulated flock” propels itself through the water and can form a free line.

These flows affect group organization in different ways—depending on the size of the group.

For small groups of up to four fliers, the researchers found an effect in which each member gets help from aerodynamic interactions to maintain his position relative to his neighbors.

“If the craft strays from its position, the eddies or eddies left behind by the leading neighbor help push the follower back into position and keep it there,” explains Ristroff, director of the NYU Applied Mathematics Laboratory, which conducted the experiment. . “This means that leaflets can be automatically assembled into regularly spaced, ordered queues without any additional effort because physics does all the work.

“However, for larger groups, these flow interactions can cause subsequent members to be pushed and thrown out of position, often resulting in group collapse due to collisions between members. This means that in some types of birds The very long groups seen in are not easy to form, and later members may have to constantly work to maintain their position and avoid bumping into neighbors.

The authors then deployed mathematical models to better understand the underlying forces driving the experimental results.

Here, they concluded that the flow-mediated interactions between neighbors are actually spring-like forces that hold each member in place—much like a train’s carriages connected by springs.

However, these “springs” only act in one direction – the lead bird can exert force on its followers, but not vice versa – and this non-reciprocal interaction means that the following members tend to resonate or oscillate violently .

“The oscillations look like waves, rocking members forward and backward, and propagate along the group and increase in intensity, causing later members to collide together,” said Joel Newbold, then a graduate student in physics at New York University. Te explained.

The team named these new waves “flonons,” which are based on a similar concept to phonons, which are vibrational waves in a system of masses connected by springs and are used to simulate the motion of atoms or molecules in crystals or other materials. .

Newbolt added: “Our findings therefore suggest some interesting connections to the physics of materials, with birds in ordered flocks analogous to atoms in regular crystals.”