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New Equation Helps Unravel Behavior Of Turbulence

October 19, 2005
Johns Hopkins University
Researchers have discovered a mathematical formula that may enable more precise models of turbulence, with practical implications in areas as diverse as weather forecasting, pollutant control, engine design and astrophysics.

Doctoral student Yi Li and Professor Charles Meneveau conduct turbulence experiments in a wind tunnel located on Johns Hopkins' Homewood campus.
Credit: Photo by Will Kirk/JHU

To most people, turbulence is the jolt felt byjet passengers moving through a rough pocket of air. But to scientists,turbulence is the chaotic flow of a gas or liquid, in which parts ofthe current curl into irregular, ever smaller, tight eddies. It's avery common phenomenon that can affect weather conditions, greatlyalter the movement of pollutants, dampen a vehicle's speed, or play arole in the way chemicals mix and combustion engines perform. Yet thephenomenon is difficult to understand, and scientists cannot easilypredict how a turbulent flow will behave.

While working on this problem, researchers at The Johns HopkinsUniversity have discovered a new mathematical formula that could leadto more precise computer models describing turbulent flow. CharlesMeneveau, a professor of mechanical engineering, and Yi Li, a doctoralstudent in the department, unveiled the formula, called the "advecteddelta-vee equation," in a paper published in the Oct. 14 issue of thejournal Physical Review Letters.

"This equation gives us a mathematical shortcut to describe a complexcharacteristic of turbulence called intermittency," said Meneveau, whoalso is director of the Center for Environmental and Applied FluidMechanics at Johns Hopkins. "It solves just one piece of the overallturbulence puzzle, but it's a very important piece."

Intermittency refers to abrupt, very concentrated changes in the speedof a moving fluid. If the velocity of a fluid is plotted on a graph,these changes look like sharp drop-offs or cliffs, rather than smooth,gentle slopes. These sharp changes are said to be intermittent becausethey occur infrequently within a turbulent flow, but when they do, theycan be quite violent.

This characteristic has been particularly tough to include incomputer models of turbulence because representing it numericallyrequires a huge number of calculations and a mammoth amount ofcomputing power. "Conceptually, we could do it," Meneveau said. "Butit's not practical."

Meneveau and Li devised a shortcut by tracking two particles as theymove with a turbulent flow like two balloons tossed along by a gust ofwind. The resulting equation gave them a tool to predict intermittencyby merely solving this simple equation rather than having to solvecomplicated computer models of turbulence. "Ultimately, we believe thiswill help researchers put together more precise models that could beused to predict weather patterns, movement within bodies of water andeven some turbulent events that take place within an internalcombustion engine," Meneveau said. "Astrophysicists are also interestedin this because, for instance, magnetic fields in interplanetary spacedemonstrate turbulence-like intermittent features."

He and his students have been conducting their own measurements ofturbulence and intermittency in a wind tunnel located on the Homewoodcampus of Johns Hopkins. Wind tunnel experiments allow them to gatherdata to provide ideas for better computer models and help them verifythat predictions from these models match up with real-world results.


Funding for Meneveau and Li's research has been provided by the National Science Foundation and the Office of Naval Research.

Related links:
Charles Meneveau's Web page:
Johns Hopkins Center for Environmental and Applied Fluid Mechanics:
Johns Hopkins Department of Mechanical Engineering:

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The above post is reprinted from materials provided by Johns Hopkins University. Note: Materials may be edited for content and length.

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Johns Hopkins University. "New Equation Helps Unravel Behavior Of Turbulence." ScienceDaily. ScienceDaily, 19 October 2005. <>.
Johns Hopkins University. (2005, October 19). New Equation Helps Unravel Behavior Of Turbulence. ScienceDaily. Retrieved November 28, 2015 from
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