Shallow water yields deep research results

	From left, research assistants Tunc Goruney, Jason Foust, and Philip Breneman work with Donald Rockwell.

An island in a river or ocean, a jet speeding across the sky, and an aneurysm in an artery or vein all create the same phenomenon—a vortex.

The swirl of water or air caused by such an object, moving or stationary, is much more complicated than it might look, says Donald Rockwell, the Paul B. Reinhold Professor of Mechanical Engineering and Mechanics.

And when vortices cover a large portion of a relatively shallow body of water, they affect the spread of pollutants, the health of aquatic life and vegetation, and more.

Rockwell leads a research team that has developed quantitative imaging techniques to study flow patterns and vortices in shallow bodies of water. He also collaborates with researchers at other universities who use numerical (computer) simulations to study the onset and development of vortices.

Recently, Rockwell gave an invited lecture at the annual meeting of the American Physical Society’s Division of Fluid Dynamics, which is regarded as the premier international meeting on basic fluid mechanics. This year’s conference was held in Tampa Bay, Fla.

Rockwell, a Fellow of the Society, titled his lecture “Vortex Formation in Shallow Flows.” The address was a sequel to a keynote lecture on the same topic that Rockwell gave in 2003 at the International Symposium on Shallow Flows in The Netherlands.

Both presentations were based on the professor’s work with members of his Lehigh research group, including Alis Ekmekci, Haojun Fu, Jung-Chang Lin, and Muammer Ozgoren.

Lehigh achieved another distinction in this area recently when articles by Rockwell’s group ranked first and fifth in a survey of the Top Ten Most Read Articles of 2006 in the prestigious Journal of Fluid Mechanics, published by Cambridge University Press.

A more sophisticated tool

	An example of the laser-based imaging technique developed at Lehigh.

The Lehigh researchers are particularly interested in coastal areas, rivers and channels, where vortices measuring hundreds of feet in diameter swirl in water as shallow as a few feet in depth.

“The instabilities that lead to the development of these vortex patterns have important consequences for the spreading and control of pollutants, the maintenance of a healthy environment for aquatic life and vegetation, and the erosion and sediment transport of the bed [bottom surface] of a coastal region or river,” Rockwell says.

Traditionally, he says, researchers studying flow patterns in shallow water bodies have injected dyes or other markers into the flows. Rockwell’s group is the first to develop laboratory systems that employ laser-based imaging techniques and image processing to make quantitative measurements of the flow patterns in shallow layers of water.

The researchers place tens of thousands of micron-sized particles in a large water channel in Lehigh’s Fluid Mechanics Laboratory, and illuminate the particles with dual-pulsed lasers. Computer-based evaluation of the images of particle patterns leads to the field of instantaneous velocity at thousands of locations within the flow.

Quantitative, laser-based imaging techniques, says Rockwell, offer researchers a more sophisticated tool than traditional imaging techniques for measuring the interaction between vortices downstream from a body (such as an island) and vortices that originate from the upstream region of the body.

As these two vortex patterns interact, they mutually reinforce one another, Rockwell says. This type of instability, which was recently discovered by Haojun Fu, can be detected and imaged using quantitative techniques, but not by traditional techniques that employ dyes or other markers.

The quantitative imaging techniques have advantages over numerical simulations, Rockwell says.

“With particle imaging using lasers, we can obtain a quantitative, time-dependent description of the flow just as we would obtain by using numerical simulations.

“But because there are so many elements to account for in complex flows, it isn’t always possible to obtain as much accurate information using simulations as it is with quantitative imaging in the lab.

“We have no doubt that quantitative imaging can, in some instances of complex flows, provide information that is not possible to obtain with computer simulations.”

By the numbers

	Rockwell, top center, and his research assistants work in the large water channel in Lehigh’s Fluid Mechanics Laboratory.

Rockwell is collaborating with researchers at Brown University and elsewhere to improve the effectiveness of numerical simulations in analyzing vortex flows.

“We are combining our quantitative imaging techniques with the numerical simulations used by other researchers, using our results as input,” he says.

Meanwhile, Rockwell’s Ph.D. students are pursuing studies of shallow flows and their applications in industry and academe.

Fu, who received his Ph.D. in mechanical engineering in 2004, is a scientist with Arryx Inc., a subsidiary of Haemonetics, an international company based in Boston that designs and manufactures automated blood-processing systems. He is using a micro (very small scale) version of the quantitative imaging technique to understand flows in simulated blood systems.

Ekmekci, who earned her Ph.D. in mechanical engineering in 2005, is a post-doctoral scientist at Purdue University, where she is using numerical computations to study complex flows, with the aim of complementing the imaging expertise that she gained at Lehigh.

Rockwell’s research has been supported consistently over the past three decades by the National Science Foundation. He has also received long-term funding from the Office of Naval Research and the Air Force Office of Scientific Research.

Other investigations of vortices underway in his laboratories include applications to unmanned air vehicles, ocean towing cables, submarine surfaces, and nuclear propulsion systems.

In a separate project funded by Arrow International, Rockwell’s team is investigating fluid flow past the tip of a hemodialysis catheter in a laboratory model of the superior vena cava of the human body.

--Kurt Pfitzer