Turbulent equation

To most people, turbulence is the jolt felt by jet passengers moving through a rough pocket of air. But to scientists, turbulence is the chaotic flow of a gas or liquid, in which parts of the current curl into irregular, ever smaller, tight eddies.

It's a very common phenomenon that can affect weather conditions, alter the movement of pollutants, dampen a vehicle's speed, or play a role in the way chemicals mix and combustion engines perform. Yet the phenomenon is difficult to understand, and scientists cannot easily predict how a turbulent flow will behave.

While working on this problem, researchers at The Johns Hopkins University developed a new mathematical formula that could lead to more precise computer models describing turbulent flow.

Charles Meneveau, a professor of mechanical engineering, and Yi Li, a doctoral student in the department, unveiled the formula, called the "advected delta-vee equation," in a paper published in the October 14 issue of the journal Physical Review Letters.

"This equation gives us a mathematical shortcut to describe a complex characteristic of turbulence called intermittency," said Meneveau, who also is director of the Center for Environmental and Applied Fluid Mechanics at Johns Hopkins. "It solves just one piece of the overall turbulence puzzle, but it's a very important piece."

Intermittency refers to abrupt, very concentrated changes in the speed of a moving fluid. These sharp changes are said to be intermittent because they occur infrequently within a turbulent flow, but when they do, they can be quite violent.

The characteristic has been particularly tough to include in computer models of turbulence because representing it numerically required a huge number of calculations and a mammoth amount of computing power. "Conceptually, we could do it," Meneveau said. "But it's not practical."

Meneveau and Li devised an equation that is simpler and eliminates the need for researchers to solve the more complicated computer models of turbulence. "Ultimately, we believe this will help researchers put together more precise models that could be used to predict weather patterns, movement within bodies of water and even some turbulent events that take place within an internal combustion engine," Meneveau said.

"Astrophysicists are also interested in this because, for instance, magnetic fields in interplanetary space demonstrate turbulence-like intermittent features."