Thinking Small to Predict Large-Scale Turbulence
By Lori Valigra
Randall McDermott’s research may sound like Gulliver’s Travels: the chemical engineer spends his days in a world of tiny flow structures, with the ultimate goal of capturing the large-scale effects of turbulence, one of the most complex – and computationally expensive – research areas of fluid mechanics.
McDermott, a PhD candidate in chemical engineering at the University of Utah, is tackling a new field of science – simulation science – which combines mathematics, computer science, and physics. McDermott is using this field to predict the chaotic behavior of turbulent flows. If he is successful, such simulations could help climate modeling and weather forecasting, have significant impact on developing cleaner power plants, and even influence astronomers who model stars and galaxies.
Examples of turbulence surround us in everyday life. Noisy faucets, puffy clouds, rumbling engines, and waves in the ocean are all evidence of fluid turbulence. The vapor rolling off a pot of boiling water is a particularly good visualization of turbulent flow. Turbulence can have positive and negative effects: If left to its own devices, it can stoke a fire wildly out of control, but if harnessed, it can allow engineers to design cars and airplanes with less aerodynamic drag, reducing wear and tear and improving fuel efficiency.
But what is turbulence really? The American Heritage Dictionary defines turbulence as “the motion of a fluid having local velocities that fluctuate randomly.” McDermott’s description, however, is somewhat different. “What motion we consider turbulent depends on scale,” he says. “Think of a rough ocean. To the naked eye, the sea is very turbulent. But, if you could zoom in closer and closer, eventually you would reach a point where the water looked like a placid lake. Here the fluid is laminar, because at such a small scale, the forces of viscosity are stronger than other disturbances.”
The unpredictable nature of turbulence has made its mathematical description challenging. Physicists believe that all the complexities of turbulent flows can be described by the celebrated Navier-Stokes equations, which were derived in the mid-1800s, and come directly from Isaac Newton’s laws of motion. They describe fluid motion down to a microscopic scale. However, even today’s most sophisticated computers aren’t powerful enough to solve these equations for large-scale turbulent flows, and until they are, some engineers say turbulence remains an unsolved problem.
“Imagine watching a fire in your fireplace for a minute. It takes us months and tens of thousands of computer hours to generate that calculation,” McDermott said, “even with models to describe the unresolved turbulent eddies.” To put that into the context of the typical Pentium-based home computer, it would take roughly 1,000 personal computers running for two days straight to produce about 10 seconds of information about a fire.