How Do Flocking Birds and Schools of Fish Move? New Research Offers Crystal-Clear Answer

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NYU News<br>How Do Flocking Birds and Schools of Fish Move? New Research Offers Crystal-Clear Answer

Study shows that group movement is akin to a soft crystalline material, with individual animals acting as “atoms”

Original<br>publication date:

Engineering, Science and Technology

Courant Institute of Mathematical Sciences

Research

Research

Research News

Photo credit: deemac1/Getty Images

Flocking birds and schools of fish are a familiar sight. While previous research has uncovered the broad dynamics driving these movements, their underlying intricacies remain a mystery.

A study by a team of New York University mathematicians offers some new insights into these phenomena. It reveals that flocks and schools behave in ways that are similar to a soft crystalline material, with individual birds and fish serving as “atoms” that are evenly spaced in a lattice-like formation.

The findings, which are reported in the journal Physical Review Fluids, offer detailed insights into the hydrodynamic and aerodynamic interactions crucial in aerospace and automotive engineering, robotics, and energy harvesting.

“Our findings offer a new way to understand how animal collectives coordinate movement and respond to their environment,” says Christiana Mavroyiakoumou, a researcher at NYU’s Courant Institute School of Mathematics, Computing, and Data Science at the time of the study and now a fellow at Oxford University’s Mathematical Institute. “More specifically, lines of birds or fish behave like an elastic material with regularly spaced individuals held together by flexible, or spring-like, bonds—akin to soft crystalline substances in which atoms are arranged in an orderly, repeating pattern.”

“Because these movements are similar to those that form the building blocks of materials, the work opens new avenues for analyzing—and potentially manipulating—how these components interact,” adds Courant Professor Leif Ristroph, director of NYU’s Applied Mathematics Laboratory, where the research was conducted.

The laboratory previously uncovered how birds and fish move together without colliding and the underlying aerodynamics of these movements. However, the detailed nature of these orchestrated motions had been less clear.

The research team, which also included Jiajie Wu, an NYU undergraduate at the time of the study, proposed a mathematical model to explain these movements—one that was akin to those of soft crystalline materials, or soft crystals. These ordered solid materials can change their properties in response to stimuli, such as temperature or physical force, which make its atomic organization fragile. The researchers, then, saw a connection between crystalline organization and how birds or fish move together while adjusting their movements and formation in response to air or water flows, predators, or objects, such as rocks or buildings.

“Crystalline organization is inherently fragile as positions are susceptible to deformations and instabilities,” explains Mavroyiakoumou. “In similar ways, birds and fish must sense and respond quickly to other forces in order to maintain long columnar formations. So while soft crystals, flocks of birds, and schools of fish are fragile in their makeup, such fragility may also be advantageous as it can be responsive to its surroundings.”

The study’s authors considered previous experiments to determine if the model matched these experimental results. Among these was an experiment that mimicked  the columnar formations of birds—in which they line up one directly behind the other—using mechanized flappers that act like birds’ wings.

Birds and fish can influence one another through the flows they generate, helping shape group flight and swimming patterns. The gray arrow pointing from right to left in front of the flyers indicates the resulting propulsive direction while the thick vertical blue lines directly above the flyers illustrate the instantaneous flapping velocity direction of each flyer, with the smaller blue arrows that follow representing wake velocity. The black dashed line indicates that the flyers are constrained to move along a one-dimensional horizontal path, one behind the other. Images of birds by Boyce Fitzgerald and Neophytos Charalambides

The wings were 3D-printed from plastic and driven by motors to flap in water, which captured how air flows around bird wings during flight. This “mock flock” propelled through water at different speeds and could freely arrange itself within a line or queue, as seen in a video of the experiment:

A live recording of the experimental apparatus in...