Concordia Mechanical and Industrial Engineering Professor Georgios Vatistas’s proof of a 125-year-old theorem of vortices has practical applications, such as possibly predicting tornadoes
At its heart, scientific exploration is about demystifying life and the universe. Scientists observe phenomena, explore their intricacies and formulate explanations based on evidence. Sometimes they arrive at basic truths, such as “all matter consists of atoms” or “the speed of light is the ultimate limit for how fast anything can go.” Other times, experimental evidence is harder to come by, and the truth is formulated theoretically or mathematically long before it can be observed and confirmed.
Concordia Mechanical and Industrial Engineering Professor Georgios Vatistas, BEng 78, MEng 80, PhD84, has confirmed a truth. In the April 30, 2008, edition of Physical Review Letters , the world’s foremost academic physics journal, Vatistas, along with Concordia Assistant Professor Kamran Siddiqui and graduate student Hamid Ait Abderrahmane, wrote about their confirmation of J.J. Thomson’s 125- year-old theorem on the stability of vortex rings. Thomson theorized that up to six (and potentially seven) naturally occurring vortices could rotate around the centre of a larger vortex.
Nature is replete with whirling masses of vortices that include tornadoes, hurricanes, spiral galaxies— and even the swirl of a flushing toilet. By experimentally demonstrating that Thomson’s treatise holds, Vatistas and his team have confirmed that it can be used to describe and/or detect an almost endless list of phenomena.
They have also demonstrated that, under the right conditions, these vortices almost have to appear. As such, the theory’s most fundamental aspects can be applied to practical situations in a predictable fashion, such as how helicopter blades might be redesigned to minimize fuselage noise or where tornadoes might occur. The findings have captured the attention of many in the world of physics and beyond.
Vatistas’s fascination with whirls and eddies dates back to his youth in coastal Greece, where he saw first-hand how strong winds and high seas could combine to produce dangerous swirling masses of water. Though warned by his grandfathers to give them wide berth, Vatistas—already an aspiring engineer—was captivated by the movement in the water. “I was making my own toy boats and sails from recycled tin and cloth and testing their stability and manoeuvrability in these currents,” he recalls.
As a teenager, his imagination was further fuelled by Homer’s Odyssey. “The clear description of the tidal whirlpool Charybdis and the river cisterns whirling around the island of Phaeacians captured my attention and curiosity,” he says.
Still, when Vatistas came to Concordia in 1974 after emigrating from Greece one year earlier, delving into the world of research to prove a century-old theorem was the furthest thing from his mind. “My plans were to complete my engineering degree, return to Greece and practice the profession, living happily ever after,” he admits. He adds with a grin, “However, life takes some unforeseen turns.”
The unexpected began with an invitation in 1977 to work at Concordia as a summer research assistant on a project about vortices. Vatistas accepted, and soon after decided to pursue a master’s degree. Next came another “unforeseen turn”: Vatistas met his future wife, Stephanie Manolakos, BA83, as he was completing his master’s and she was beginning undergraduate studies at Concordia. Their relationship solidified his connection to both Montreal and the University. He soon completed his PhD at Concordia and became a faculty member in 1985.
Four years later, Vatistas was exploring the properties of combined vortices by swirling up liquid in tall, slender cylinders. By examining the central funnel from above, he hoped to learn something about particle concentrations. Instead of the relatively smooth-sided funnel he was expecting, waves undulated up along the length of the core, thereby obstructing his vie In an attempt to minimize this visual interference, Vatistas lowered the liquid height to work with a much shallower pool. When he spun up the liquid again, the core eventually formed a polygonal, triangular shape. He remembers his first reaction to this geometric beauty as a rather unscientific, “Wow-w-w-w!”—which reflects his boyish enthusiasm.
Upon witnessing the phenomenon, Jean Wang, one of Vatistas’s PhD students, asked how his professor had managed to fabricate the beautiful solid insert in the liquid. Vatistas replied that it was nature alone producing the shapes. While the triangular core told him precious little about particle concentrations, it captured his imagination, much like the whirlpools of his youth.
Back in time
A review of the literature sent Vatistas back to an 1883 treatise by physicist J.J. Thomson (1856-1940), recipient of the 1906Nobel Prize in Physics. Thomson was recognized for his work on the structure of the atom and identification of the electron. He mathematically demonstrated what should occur in systems of point vortices or masses. To understand Thomson’s conclusions, picture the satellite image of a hurricane.
The eye is the core of a huge, whirling mass of air and water that extends outward, sometimes hundreds of kilometres, from the centre of the storm. Pressure differences at the edge of the hurricane’s eye—where the air inside and outside of it collide—can actually spin off other vortices, in the form of tornadoes, which orbit the eye until they dissipate. Under ideal circumstances, Thomson predicted that naturally occurring stable systems of up to six—and potentially seven—vortices could rotate around the core of a larger spinning mass.
The mathematician Thomas Havelock (1877-1968) later underlined a distinct relationship between the radius of the parent vortex and those of its daughters. Vatistas suspected that the triangular polygon he produced in 1989 was indeed a manifestation of Thomson’s treatise, where three daughter vortices were equally distributed around the parent’s core. He even managed to produce the square, pentagonal and hexagonal cross-sectional cores predicted for four, five and six daughter vortices. Unfortunately, at that point, the system appeared to give over to turbulence.
Recently, Vatistas, Siddiqui and Abderrahmane decided to leverage advances in image processing and experimental equipment to revisit the issue. This time, they were able to see further and confirm the two key elements of Thomson’s earlier conjecture. First, they reproduced the initial results and established their stability. In their experiment, the vortex and its daughters quickly re-formed even after they used a stick to disrupt the water flow.
Vatistas describes that while more daughter vortices are produced as the velocity of the parent vortex increases, the range of velocities over which the system is stabilized decreases. “With six daughter vortices, the stability exists only in a very narrow range. You have to look quickly or you miss it,” he explains. Seven daughter vortices are theoretically possible but are practically impossible, he adds, because the range of frequencies at which they occur is so narrow that the chances of observing them are infinitesimally small. “It’s like trying to balance a pencil o n a very sharp tip,” he analogizes.
Second, the team confirmed the relationship between the parent and daughter radii. In 2000, the research team of Dan Durkin and Joel Fajans at the University of California, Berkeley, demonstrated the stability of the cross-sectional cores in electron columns. Vatistas and colleagues made the confirmation using a normal fluid (water), corroborated all the relevant aspects of the phenomenon and even went beyond the original mathematical theory. “This is where we have clearly established a first,” Vatistas says. Thomson’s conjecture had long been assumed to be valid, and had been used to explain phenomena as varied as superfluidity, magnetism, electron plasmas and planetary atmospherics. Its widespread applicability was confirmed by Paul Williams, a professor at the University of Reading in the United Kingdom, who integrated the theory to the study of polar circulation. “It turns out that there is a very intimate connection between the fluid dynamics of a freshly stirred cup of tea, and those of an atmosphere on a rotating planet,” Williams wrote in a 2003 paper.
Vatistas’s discovery is already being applied. It’s lending credence to a theory of tornados by Alfred Bedard, a scientist at the National Oceanic and Atmospheric Administration in Colorado. Bedard specializes in the sound signatures of natural events. During the course of an experiment on the acoustics of avalanches, he noticed that some of his sensors had picked up very distinctive, low frequency sound waves that seemed unrelated to the snowfalls under study. Low frequency waves have extremely long wave lengths and can travel significant distances—hundreds, sometimes thousands, of kilometres—from their origin.
Known as infrasound, the waves can only be detected by sensors because they occur below the level of human hearing. Unsure where the waves had come from, Bedard began looking at earthquake and meteorological data from around the United States for their potential source. He discovered that a series of tornadoes had occurred several hundred kilometres away slightly after his measurements had been taken. Bedard is now fairly certain that the distinct sound signatures were created by daughter vortices rumbling off a parent tornado as it formed high up in the Earth’s atmosphere.
“He says that, through this method, we can detect tornados earlier than with radar,” Vatistas explains. He adds that it’s the daughter vortices of hurricanes, tornadoes and typhoons that wreak so much havoc. “They impact the behaviour of the larger storm, causing huge moving loads on structures—like bridges and buildings—which are very dangerous,” Vatistas says. “Ultimately, understanding this phenomenon can help us improve the design of buildings.” It can also facilitate the design of structures in which vortices are caused to occur, such as tubes leading to water turbines in hydroelectric dams.
It’s not surprising, then, that the confirmation is making waves in the physics and engineering worlds. Vatistas has been interviewed by numerous publications, including the prestigious Physics World (May 8, 2008).More unexpected has been the mainstream media’s interest in his team’s work. Articles have appeared in local Montreal daily newspapers, such as Le Devoir and La Presse , in national and international publications and on many websites.
Clearly, all the attention tickles Vatistas. “Following the worldwide publicity and my interview with CBC Radio’s science program, Quirks and Quarks , I was flooded with emails from experts, as well as from ordinary people who were genuinely interested in the discovery. Physicists, mathematicians, architects, social scientists, engineers, classicists, professors, graduate and high school students, and others wanted me to expand on and/or provide additional information about the phenomenon,” he says. “Most of the questions had to do with the unaccounted-for hexagonal weather formation in Saturn’s north pole, a likely manifestation of the phenomenon. Others dealt with the details about the natural phenomenon, with the organizational structures in natural occurrences, artistic designs in nature, galactic disk formations and much more.”
Images of the vortex patterns will be featured this fall in the new edition of The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press), a book by well-known science writer Philip Ball. Vatistas says he is also pleased his work shines the spotlight on Concordia. “It‘s very satisfying to give back to the institution that has also given me a superb universal education. I believe this discovery is an indication that our Faculty of Engineering and Computer Science is scientifically very strong,” he says.
“It is so gratifying to have been able, along with my colleagues, to validate a theoretical conjecture made by one of the world’s most renowned physicists,” he enthuses. “At the same time, I have a sense of responsibility to continue the work.”
Vatistas points to the praise he received from Richard Packard, a respected physics professor at the University of California, Berkeley. In the May 8, 2008, issue of Physics World magazine, Packard was quoted as saying, “I do find it fascinating that vortices, which occur in so many places in nature, are still the object of research after over 200years of scrutiny by some of the best minds in science.”
While Vatistas continues to manage the interest his confirmation has generated, he is already planning his next steps. The association of these phenomena to the same set of equations indicates the potential that something deeper, and more fundamental, connects them. He’s determined to find exactly what it is.
Dawn Wiseman, BEng 91, GrDip 96, MA 02, is a Montreal-based writer.
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Howard Bokser, 514-848-2424 ext. 3826, Howard.Bokser@concordia.ca