A new study by mathematicians has uncovered previously unknown aerodynamic interactions that help explain how birds fly in coordinated flocks. The findings, published in the journal Nature Communications, shed light on how animals like birds and fish move together in groups and could have applications in transportation and energy.
“This area of research is important since animals are known to take advantage of the flows, such as of air or water, left by other members of a group to save on the energy needed to move or to reduce drag or resistance,” said Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and the study’s senior author.
Flock Size Matters
The researchers found that the impact of aerodynamics depends on the size of the flying group. In small groups of up to about four birds, the aerodynamic interactions help each member maintain its position relative to its neighbors. If a bird is displaced, the swirls of air left by the leading bird help push the follower back into place.
“This means the flyers can assemble into an orderly queue of regular spacing automatically and with no extra effort, since the physics does all the work,” Ristroph explained.
However, in larger groups, these same flow interactions can cause birds in the back to be jostled around and thrown out of position, potentially leading to collisions and a breakdown of the flock formation.
Flonons: A New Type of Wave
To better understand the forces at play, the researchers used mathematical modeling. They concluded that the flow-mediated interactions between neighboring birds act like one-way springs, with a lead bird exerting force on its follower but not vice versa. This non-reciprocal interaction can cause later members to oscillate wildly.
“The oscillations look like waves that jiggle the members forwards and backwards and which travel down the group and increase in intensity, causing later members to crash together,” said Joel Newbolt, a former NYU graduate student in physics who worked on the study.
The team dubbed these new types of waves “flonons,” drawing a parallel to phonons, which refer to vibrational waves in systems of masses linked by springs and are used to model the motions of atoms or molecules in crystals or other materials.
“Our findings therefore raise some interesting connections to material physics in which birds in an orderly flock are analogous to atoms in a regular crystal,” Newbolt added.
The study’s findings expand our understanding of how animals move in groups and could have applications in fields like transportation and energy, such as more efficient propulsion through air or water and better harvesting of power from wind, water currents, or waves.
