(CN) - Researchers from the University of Illinois have fully modeled the transition of fluids from turbulent to calm phases, advancing a theoretical understanding that has confounded scientists for well over a century.
The team was able to measure the transitional effects of laminar, or calm, fluids as they convert to a turbulent phase, which resembles the progression toward ecological extinction for different species.
Physicist Nigel Goldenfeld, along with graduate students Hong-Yan Shih and Tsung-Lin Hsieh from the University of Illinois at Urbana-Champaign, ran computer simulations of pipe flow to measure and analyze interactions within liquids. This led the group to realize the parallels between laminar-turbulent phase transitions and the predators and prey dynamic.
"To our surprise, we found that such a relationship is like the predator population. Once turbulence is reduced by zonal flow - just as prey are killed by predators - the zonal flow has a lack of source and thus decreases, in the same way that predator population decreases due to insufficient prey," Shih explained in an email.
The researchers learned that only two classes of fluid motions were required to transition the turbulence and laminar phases: turbulence along the pipe's center, and a large swirling vortex - which is referred to as zonal flow - around the interior of the pipe. This resembles the jet streams that circle around the Earth.
In order to bypass previous experimentation hurdles that have stalled progress since 1883, the researchers approached the study by thinking about phase transition.
Doing this allowed them to apply concepts and mathematical techniques for phase transition to population biology and statistical mechanics. Phase transition can be exemplified as the universe cooling after the Big Bang, or ice melting into water.
"We confirmed our idea by performing computer simulations on fluid, and we built up a simple and minimal ecological model to explain and reproduce the most precise experiments ever done on the laminar-turbulent transition," Shih said.
This allowed Goldenfeld, Shih and Hsieh to corroborate that their ecological model was mathematically equivalent to a model called directed percolation, which had been previously hypothesized as a description for the laminar-turbulent transition.
"The connection between directed percolation and transitional turbulence was previously demonstrated by Maksim Sipos and Dr. Goldenfeld through computer simulations," Shih explained. "From our new findings we understand that such a connection applies to both turbulence and ecology."
These findings can also be applied to the transportation of oil, which is often rigorous and expensive.
"Turbulence is usually unwanted because it creates more friction drag than laminar flow and thus causes more energy loss during transport of oil or gas through pipelines. Our work may help discover a way to suppress turbulence in pipes, thus reducing energy cost," Shih said.
Balancing the laminar-turbulent transition can also aid in the prevention of cardiovascular issues.
"Turbulent transition in blood flow can be a deadly cause of ruptured aneurysms in the heart," Shih explained. "Our work may suggest ways to control turbulence-bursting and thus lessen the risk of aorta or vein rupture in the heart."
Further experiments must be conducted in order to further demonstrate the group's findings, which would determine if turbulence-induced zonal flow could suppress and regulate the onset of turbulence due to the predator-prey mechanism. Physically based pipe experiments could validate their computer simulations.
"We think that it can be tested with different setups in experiments. Once it is confirmed, further theory and experiments can study how to specifically control turbulence in various experimental systems," Shih said.
The researchers published their findings online in "Nature Physics."
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