New Equation Helps Unravel Behavior Of Turbulence

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: http://www.me.jhu.edu/~meneveau
Johns Hopkins Center for Environmental and Applied Fluid Mechanics: http://www.jhu.edu/~ceafm/
Johns Hopkins Department of Mechanical Engineering: http://www.me.jhu.edu/