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Big Crowds Flow Like Water in Amazing (and Terrifying) Ways

Hydrodynamic theory helps to explain how large human crowds flow like water.

Wikipedia/Creative Commons
New York City marathon runners on the Verrazzano-Narrows Bridge.
Source: Wikipedia/Creative Commons

Large human crowds exhibit fluid-like collective behavior that can be predicted based solely on hydrodynamic theory, according to a new study (Bain and Bartolo, 2019) published today in the journal Science. This pioneering research shows, for the first time, how crowds of people flow like water in ways that appear to override so-called “interaction rules” between individuals.

This paper, “Dynamic Response and Hydrodynamics of Polarized Crowds," was co-authored by Nicolas Bain and Denis Bartolo of the Laboratoire de Physique in Lyon, France. Bain is a Ph.D. student in physics at the ENS de Lyon working under the supervision of Bartolo. The groundbreaking research presented in this paper focuses on studying human crowds from an active matter physicist’s point of view.

For this large-scale research on human crowd movement through the lens of hydrodynamic theory, Bain and Bartolo set up cameras at a birds-eye view so they could film the flow of thousands of marathon runners being sectioned off into different corrals at the starting line of three of the world’s largest marathons in Chicago, Paris, and Atlanta.

For this study, the researchers focused on the entire crowd as a singular entity and applied hydrodynamic theory to human crowd movement that was free of individual behavioral assumptions. The authors sum up their study's design and significance:

Mesmerizing impressions of virtually all patterns observed in bird flocks, fish schools, insect swarms, and even human crowds are effectively rendered in silico by simple algorithms. Going beyond visual impressions and predicting the collective dynamics of groups of living creatures in response to physical, social, or biological imperatives, however, remains a formidable challenge.

Modeling crowd motion is central to situations as diverse as risk prevention in mass events and visual effects rendering in the motion picture industry. We use tens of thousands of road-race participants in starting corrals to elucidate the flowing behavior of polarized crowds by probing its response to boundary motion. Building on these observations, we lay out a hydrodynamic theory of polarized crowds and demonstrate its predictive power. We expect this description of human groups as active continua to provide quantitative guidelines for crowd management.

As you can see in the video below, when Bain and Bartolo analyzed the collective movement of swarms of marathon runners at the starting line of a race, they were able to identify waves of crowd density and velocity that created a ripple effect that would cascade from the back and front of the line, but not from side to side. Unlike some life-threatening "crowds flowing like a tsunami" situations that I will discuss later in this post, the thousands of marathon runners participating in these well-organized running events slowly make progress toward the starting line under the clearly articulated guidance of race-day staffers.

Interestingly, the "hydrodynamic wave" of marathon runners waiting to start a 26.2-mile run appears to ripple through the crowd at a constant speed. Using predictive mathematical models, the researchers were able to accurately predict how these dynamics would play out from one marathon starting line to another.

A noteworthy perspective piece about the new study by Bain and Bartolo, "Flowing Crowds" by Nicholas Ouellette of Stanford University, was also published in the Jan. 4 issue of Science. Oullette is the founder and director of Stanford’s Environmental Complexity Lab, which focuses on self-organization in complex systems with relevance to collective behavior and experimental fluid mechanics, such as the turbulent fluid flow and collective motion in animal groups and large human crowds.

Oullette summed up the significance of this research on crowds acting like water in his perspective article,

"On p. 46 of this issue [of Science], Bain and Bartolo (4) describe a powerful new way to model human crowds. Instead of focusing on individuals, they build a continuum “hydrodynamic” model of the crowd as a whole and then constrain it with observational data collected from marathon runners. This approach circumvents many of the sometimes-questionable assumptions that have previously been made and provides a roadmap for constructing an empirically grounded theory of collective behavior."

Have You Ever Been "Swept Away" in a Sea of Humanity That Felt Like a Tidal Wave?

While I was reading about the latest research on large crowds flowing like water and behaving in predictable patterns based on hydrodynamics, I had flashbacks to specific circumstances in both sports and daily life where I've experienced this phenomenon. In the second part of this post, I'm going to shift gears and share some autobiographical stories and audio-visual examples that corroborate the latest findings by Bain and Bartolo on the hydrodynamics of human crowds.

Before reading further: Can you recollect any firsthand experiences of feeling a massive wave of human beings acting like a wall of water that made you feel powerless about choosing which direction your body was going to move?

When I asked myself this question earlier today, four examples sprang to mind. Two of them were memories that made me feel good; the other two triggered some post-traumatic stress. After reading the latest study by Bain and Bartolo, I realize that the closest I've come to thinking I was going to die was in situations where the water-like movements of a massive crowd — who had no idea that their collective actions were creating life-threatening danger — almost annihilated individuals in a distant part of the group.

As a marathon runner, I've experienced the exact wave-like phenomenon that Bain and Bartolo captured on film for their latest study as a participant being "herded" by race-day volunteers into a starting corral. For me, this experience has always been a joyful, camaraderie-building experience. The most exuberant "E pluribus unum" sense of being a drop of water in a sea of humanity is when I'm among 50,000+ marathon runners at the starting line of the world's largest marathon in New York City.

As you can see in the video above, the first mile of the NYC marathon takes runners from Staten Island to Brooklyn via the Verrazano-Narrows Bridge. Being shoulder-to-shoulder and running stride-for-stride with other marathoners during this portion of the NYC marathon feels like surfing a wave. This is the only time during a marathon when it feels like my feet aren't even touching the ground, and I'm being carried forward by a gigantic wave of strangers working towards a common goal. This is a life-affirming experience.

As a native New Yorker, there are countless times that I've also experienced the "sea of humanity" pushing my body to and fro in ways that were beyond my control while commuting on the subway during rush hour. Anyone who has gotten on or off an MTA train heading in or out of Manhattan during rush hour has probably felt the hydrodynamics of crowds flowing like water.

For most of my life, I lived on 14th Street and took the L train regularly. Although most people hate the rush-hour crowds, for some weird reason I've always loved being packed into a subway car like sardines. In a metropolis where it's so easy to be surrounded by people but feel physically isolated, being crammed onto a subway car always creates a strange kind of forced intimacy that feels bizarrely comforting to me.

That said, as you can see in the video above, the type of water-like dynamics observed by Bain and Bartolo at marathon starting lines are also observable in this exhibit of commuters getting plugged up (like a blocked drain in need of a plunger) on the stairs leading to the platform at Union Square, which is often filled to the rim. The amoeba-like dynamic of the crowd as a single entity coagulates, which stops flow in both directions. Obviously, these hydrodynamics of a crowd not flowing smoothly in underground tunnels creates very real dangers for everyday commuters.

Another autobiographical example of feeling a large human crowd flow like water occurred while I was submerged in water during a life-threatening situation in which I almost drowned. Recollecting this event from two decades ago still gives me a PTSD-like panic attack that takes my breath away.

On the morning of August 15, 1999, I put on my wetsuit along with about 2,000 other Ironman triathletes to compete in the inaugural Lake Placid triathlon. The 2.4-mile swim leg of these long-distance swim, bike, run events usually takes place in the ocean, where there is plenty of space to spread out.

Unfortunately, as the name of this particular triathlon suggests, the swim leg at Ironman Lake Placid takes place in a relatively small lake, and the race was oversold. Because of the cramped conditions, swimmers had to do a short .6 mile out-and-back twice; this meant athletes literally had to swim over each other if they wanted to get from point A to B by covering the shortest distance of a straight line. Additionally, the shoreline of the lake was too small to accommodate thousands of athletes. As you can see in the video below, in the early days of Ironman Lake Placid, this swim start was complete chaos and created really hazardous conditions.

Just like Bain and Bartolo describe in their research on marathon runners waiting to start a race in different chutes, once the group of swimmers was in motion, they became like a collective wave or rip current that wasn't guided by individual intentions. Because all the triathletes at the starting line were heading for the same turn-around buoy on the horizon, there was no way for the smaller stream of swimmers trickling in from the left to merge with the tsunami of athletes gushing in from the right.

When I did Lake Placid back in '99, I got trapped a few feet underneath a collective mass of slippery black neoprene worn by hundreds of swimmers coming in from the right side of the lake like a tidal wave. It was impossible to breathe. These swimmers were all in a big flow channel that kept them surging forward together en masse. Due to bad luck and not understanding how the fluid dynamics of this crowded swim would work, I was stuck on the left side, where a bottleneck formed, and there was no flow.

With huge quantities of water churning and complete mayhem at the starting line of this first-time event, nobody even knew that a few unlucky athletes were trapped with me in a whirlpool that was created by the opposing currents of swimmers in different flow channels. All of the cheering, splashing, and rushing adrenaline of athletes and spectators made it impossible for anyone to communicate sensible instructions once the starting gun was fired. The Ironman Lake Placid swim start is the closest I've ever come to losing consciousness and thinking I was going to die in an athletic competition. It was terrifying.

As Bain and Bartolo warn in the conclusion of their paper on the fluid-like behaviors of large crowds,

"We show that reorienting the direction of motion of a polarized crowd at once is impossible when relying only on locally accessible signals. Orientational cues must be provided to the entire assembly to change its direction of motion. We also predict the time it takes to set in motion, or to stop, a crowd of a given extent by providing information at its boundary."

Based on these hydrodynamic principles, there was no way for race volunteers to give orientational cues to thousands of polarized swimmers once they were in motion. Thankfully, in 2013, Ironman race organizers began to change the mass-start format of the swim to a rolling start of smaller waves, which lets swimmers trickle out of corrals in a staggered fashion that significantly reduces risks.

In a statement, the organizers of Ironman North America said, "Both Ironman Coeur d’Alene and Ironman Lake Placid will feature rolling starts in 2013. Athletes will enter the water in a continuous stream through a controlled access point, similar to how running road races are started. An athlete’s times will start when they cross timing mats under the swim arch."

The final example of hydrodynamics and big crowds flowing like water in a way that caused some bodily harm (and maybe almost killed me) occurred at a general admission concert by The Clash in 1982. When I went to see The Clash at Cape Cod Coliseum in August of '82, their song "Rock the Casbah" was a top-10 hit on the Billboard Hot 100. Everyone at the concert was amped-up and extremely enthusiastic to see this chart-topping British band.

From a crowd dynamics perspective, the problem with Cape Cod Coliseum (which closed in 1984) was that the owners had haphazardly converted an old ice skating rink into a concert venue without giving much thought to crowd safety. Because the concert was general admission with no assigned seats, everyone crammed onto the main floor, which became a mosh pit.

When I went to this Clash concert as a teenager, I arrived early to be near the front of the crowd. Unfortunately, this meant I got wedged up against a concrete barrier near the stage and was pinned there just a few songs after the concert began. To this day, whenever I hear "Magnificent Seven," the unique drum beats of this song remind me of the rhythmic pulse I felt with each wave of exuberance from the crowd smashing my body against the concrete barrier. Each wave of collective movement from the sold-out crowd pushed my lower body against the waist-high blockade with more and more force in a way that felt like it might split me in half. Luckily, some security guards finally started pulling people up over the barrier before we were pulverized by the sea of humanity unwittingly crushing us in waves that started at the back of the arena.

In the video below, lead singer of the Clash, Joe Strummer, describes watching fluid-like collective movements of big crowds at Shea Stadium from his vantage point on stage.

My personal encounter with a wall of people almost crushing me at a rock concert occurred a few years after The Who concert disaster in 1979. The New York Times reported on this incident in an article, "11 Killed and 8 Badly Hurt in Crush Before Rock Concert in Cincinnati." This article describes the dangerous water-like rush of a massive crowd: "At the time of the incident, eight of the coliseum's many doors had reportedly been opened, creating consternation among the fans lined up outside one door at the southwest corner, which remained shut. The police later said coliseum officials failed to open enough doors to handle the crowd. As the doors sprang open and the fans rushed forward, many fell and were trampled."

The latest research on the hydrodynamics of crowd flow by Nicolas Bain and Denis Bartolo could save lives. As the authors conclude, "The description of crowds as continua should be useful to elucidate their response to large-amplitude perturbations and their transitions from flowing liquids to amorphous solids, two situations where crowd dynamics become hazardous.”

Facebook Image Credit: Beeboys/Shutterstock


Nicolas Bain and Denis Bartolo. "Dynamic Response and Hydrodynamics of Polarized Crowds." Science (First published: January 4, 2019) DOI: 10.1126/science.aat9891

Nicholas T. Ouellette. "Flowing Crowds." Science (First published: January 4, 2019) DOI: 10.1126/science.aav9869

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