Observing the water flowing from the faucet has brought new breakthroughs in the study of turbulence and transitional flow!

The water that flows out of an ordinary faucet tells a complicated story about its journey through pipes. At high pressure and speed, the flow from a faucet is turbulent: chaotic and disordered, like crashing ocean waves. Compared to ordered laminar flow, such as the steady flow from a faucet at low pressure and low speed, scientists know relatively little about turbulent flow. Even less is known about how laminar flow becomes turbulent. Transitional flow is a mix of ordered and disordered flow, which occurs when a fluid moves at intermediate speeds.

Now, Dr. Rory Cerbus, Dr. Chien-Chia Liu, Dr. Gustavo Gioia, and Dr. Pinaki Chakraborty of the Institute of Fluid Mechanics and Continuum Physics at the Okinawa Institute of Science and Technology Graduate University (OIST) have drawn from decades of conceptual theories of turbulence to develop a new approach to study transitional flows. Their findings, published in the journal Science Advances, may contribute to a more comprehensive and conceptual understanding of transitional flows and turbulence, with practical applications in engineering. Turbulence is often touted as the last unsolved problem in classical physics because there is something mysterious about it.

Finding order in disorder

However, under idealized conditions, we have a conceptual theory that helps explain turbulence. In the study, scientists are working to understand whether this conceptual theory might also shed light on transitional flows. Scientists have long been fascinated by turbulence. In the 15th century, Leonardo da Vinci described turbulence as a collection of eddies, or gyres, of various sizes. Centuries later, in 1941, mathematician Andrei Kolmogorov developed a conceptual theory that revealed order behind the seemingly disordered energetics of vortices. As depicted in da Vinci's sketch: A stream dropped into a pool of water initially forms a huge vortex.

This vortex quickly becomes unstable and breaks up into progressively smaller vortices. Energy is transferred from the large vortex to smaller and smaller vortices until the smallest vortex dissipates the energy through the viscosity of the water. By capturing this image in mathematical language, Kolmogorov's theory predicts the energy spectrum, a function that describes how kinetic energy is distributed among vortices of different sizes. Importantly, the small-vortex energetics are universal, meaning that although the turbulence may look different, the smallest vortices in all turbulent flows have the same energy spectrum. It's truly remarkable that such a simple concept can elegantly illuminate a seemingly intractable problem.

But there's a problem. Kolmogorov's theory is widely believed to apply only to a small set of idealized flows, not to flows in everyday life, including transitional flows. To study these transitional flows, experiments were conducted on water flowing through a 20-meter-long, 2.5-centimeter-diameter glass cylindrical pipe. The researchers added small hollow particles with roughly the same density as water, allowing them to visualize the flow. The study also used a technique called laser Doppler velocimetry to measure the vortex speeds in the transitional pipe flow. From these measured velocities, an energy spectrum was calculated. Surprisingly, the researchers found that despite looking very different from turbulence, the energy spectrum was very similar to turbulence.

But the energy spectrum corresponding to the small eddies in the transitional flow is consistent with the universal energy spectrum in Kolmogorov's theory. This discovery not only provides a new conceptual understanding of transitional flows, but also has applications in engineering. Research over the past two decades has shown that the energy spectrum can help predict the friction between water flow and pipes, which is a major concern for engineers. The greater the friction in the pipe, the more difficult it is to pump and transport fluids like oil. The research combines profound mathematical ideas with factors that engineers care about, and also found that Kolmogorov's theory has a wider applicability than anyone imagined. This is an exciting new insight into turbulence and the transition to turbulence!

Bokeyuan｜www.bokeyuan.net

Bo Ke Yuan | Research/Source: Okinawa Institute of Science and Technology

Reference journal: Science Advances

DOI: 10.1126/sciadv.aaw6256

BoKeYuan｜Science, technology, research, popular science