# Fluid Dynamics And Mathematics Used To Study Penguin Huddles

November 19, 2012

By Alan McStravick for redOrbit.com – Your Universe Online

If you fell in love with the movie “March of the Penguins”, you are in good company. Francois Blanchette, a mathematician at the University of California – Merced (UCM) found inspiration in this masterful and adorable documentary for his new study that was published this week in the online open source journal PLOS ONE. The researchers will also discuss their findings at the annual meeting of the American Physical Society’s (APS) Division of Fluid Dynamics (DFD) this week in San Diego, California.

In particular, Blanchette was struck by the masses of penguins who all huddled together to protect themselves from the bitter cold and icy winds of Antarctica. Their actions are performed, en masse, to secure enough warmth for the group that they might survive the bitter cold conditions.

Blanchette and his mathematician colleagues at UCM devised a model of penguin huddles that made the assumption that each individual penguin acted, in self-interest, to minimize its own heat loss. What the model shows is that this self-centered behavior ends up resulting in an equitable sharing of heat among the group.

Though Blanchette typically focuses on fluid dynamics, upon seeing “The March of the Penguins”, he saw how similar factors that affected the huddle dynamic, including wind and heat flow, fell within his particular area of expertise.

Along with his fellow researchers Arnold Kim and Aaron Waters, Blanchette first modeled penguin huddles that were packed so tightly together that only the penguins on the outside of the huddle were able to move. In this model, all heat generated by the penguins was dissipated by the blowing wind. In consideration of factors like the total number of penguins in the huddle along with the strength and turbulence of the wind, the model calculated which penguins on the outside of the huddle were the coldest. The coldest penguin would then move to the most sheltered spot inside the huddle. After this movement, the head distribution of the huddle was recalculated. As the model progressed, the huddle was shown to elongate and move, ever so slightly, downwind over time.

What the researchers realized was that their initial model had assumed a perfectly steady wind pattern and identical penguins. These factors were responsible for producing the longer, thinner huddle shapes than what has been noted in nature. It wasn’t until after the team introduced uncertainty into the mix, like irregular wind eddies and natural differences in size and cold tolerances of individual penguins, that their modeled huddles began to form and act like real huddles.

After perfecting the model, Blanchette and his team were able to mine it for data. What they found was that penguins shared warmth nearly equally among themselves. “Even if penguins are only selfish, only trying to find the best spot for themselves and not thinking about their community, there is still equality in the amount of time that each penguin spends exposed to the wind,” according to Blanchette. This huddle system is unique because not all instances of selfish behavior will result in as fair an outcome, he notes. “A penguin huddle is a self-sufficient system in which the animals rely on each other for shelter, and I think that is what makes it fair. If you have some kind of obstacle, like a wall, then I think it would stop being fair,” Blanchette stated.

Now that their model has accurately portrayed the penguin huddles, the researchers are seeking feedback from biologists to help them further perfect their mathematical model. The difficulty, as the team sees it, is in the gathering of experimental data. “Penguins huddle during blizzards, when the conditions are horrible, and if you’re going to collect data you’re also going to be in a blizzard in horrible conditions,” Blanchette points out. What the team hopes their model might aid in is an understanding that might guide scientists in the field. By using their model, scientists would know which observations were necessary to make to further test the model.

Blanchette and his team have stated that their model could also be used in future studies to investigate other biological organisms, such as certain bacteria, that move as a group in response to an outside stimulus like food or the presence of a toxin. Additionally, future use of the model could help in the design of swarming robots that shelter each other from harsh conditions. But that is for the future. Blanchette is still reveling in the afterglow of the publishing of his study. “Nearly everybody seems to love penguins and not enough people love math,” he says. “If we use math to study penguins we could potentially teach more people to love math too!”