UB Professor's Theory On Turbulence Questions One That Has Been Accepted For 50 Years

BUFFALO, N.Y. -- A turbulence theory developed by University at Buffalo researchers about how flows adjust near a surface and disputing a theory that has been the standard for 50 years is generating interest among mechanical and aerospace engineers.

During the next few weeks, William K. George, Ph.D., professor of mechanical and aerospace engineering at UB and director of UB's Turbulence Research Laboratory, will deliver invited talks about his theory at the University of Minnesota, Queens University, the University of Notre Dame and the Illinois Institute of Technology.

George's approach has received important support from the work of G. J. Barenblatt, Ph.D., of Cambridge University, who uses different methods to reach similar conclusions.

George's theory, first introduced at a meeting of the American Physical Society in 1988, addresses the way engineers think about problems relating to turbulent flows, including crucial aspects of vehicle design, particularly calculations of drag on large ships and aircraft.

"The turbulent boundary layer has been regarded as one of the few problems in turbulence that was well-understood. Our work calls the fundamental assumptions of that work into question and offers a new approach to the problem," said George.

Boundary layers are thin regions near any surface where the flow of gases (or liquids) must adjust from the undisturbed airstream further away from the surface. Because most boundary layers of concern to engineers are turbulent, these flows are characterized by chaotic fluctuations in velocity, which means they may only be described in terms of averages, according to George.

"Boundary layers are a consequence of viscosity -- even air, like oil, has viscosity, though far less -- and the 'no-slip condition,' which results from it, causes all flows to come to a screeching halt at a surface," he explained.

Turbulent boundary layers are part of engineering problems ranging from meteorology, involving atmospheric flows; to mechanical engineering, involving flows around aircraft and inside engines, to civil engineering, involving flows near structures. Regardless of the type of problem, though, all use as a reference the standard turbulent boundary layer, or the so-called classical model.

First proposed in the 1930s by Theodore von Karman, the legendary California Institute of Technology engineer, this theory has become the accepted standard against which engineers test boundary-layer turbulence models.

George first revisited this classical model in the 1980s, when he chose it as the subject of a talk he was invited to give at the University of Minnesota.

"My concerns about this model went all the way back to when I was a student," he said. "I never liked the classical model, it never made sense to me."

At the same time, George was working on the problem of the atmospheric boundary layer.

"As I worked on it, I realized that the questions I was asking to solve that problem were related to the ones that should be asked about the classical model," he said. "People think scientists look for the right answers, but actually we're looking for the right questions."

George and his students spent several years studying the basic assumptions of the classical model. They concluded that von Karman had started with a faulty assumption.

George explained that the boundary layer has an inner part and an outer part.

"You have to model them differently, but von Karman picked the wrong model for the outer part, so he got what we think is the wrong answer," he added.

George and his students examined the character of the fundamental equations of the boundary layers.

They began by postulating an Asymptotic Invariance Principle. The idea behind the principle is that if a theory is correct, then when taken to its limits, it should eventually satisfy Newton's law or another equation that describes fundamental phenomena.

"I concluded that von Karman's model didn't have the right physical properties," he said. "When you pushed it to its limit, it didn't give the right answers."

The fact that the classical model didn't satisfy Newton's Second Law for boundary-layer flows was not unknown, George said, but the model had, for the most part, been accepted because it seemed to generally agree with the data that was available at the time.

"People had managed to bury their reservations about it," he said. "We realized the intellectual inconsistency in it and found a different way to do it."

George conducted his research with Luciano Castillo, a UB graduate student, and Pierre Knecht, a former UB graduate student.