Undergraduate Research

Tiny bubbles calm the waters

by Marcia Goodrich

Rachael Barlock holding sand.

Rachael Barlock’s scale model of a stilling basin reduced scouring
in the sandy "riverbed" below.

Tiny bubbles in the wine may make you feel happy, but they’re nowhere near as useful as the tiny bubbles Rachael Barlock puts in rushing water.

Barlock’s bubbles can keep a raging torrent from eroding deep holes in a riverbed, a process called scouring. Her project is funded by the South Florida Water Management District, which wants to curb scouring downstream from its stilling basins. The purpose of a stilling basin is to still the water flowing into a river, often from a dam or other man-made structure. Usually, stilling basins do their job just fine. Sometimes, however, they are overwhelmed by the weather. “We’re modeling for a hundred-year storm,” Barlock says.

Barlock, a senior majoring in environmental engineering, got involved in the project through an undergraduate class taught by Brian Barkdoll, an associate professor in the Department of Civil and Environmental Engineering. “I was really interested in working with an actual client,” she says.

Building on work started by graduate student Ted Champagne, she began testing different ways of using bubbles to combat scouring. In her lab, Barlock works with a one-thirtieth-scale model of an actual basin in Florida.

Most of the experiment’s action takes place at the end of the stilling basin. There, Barlock places a long, hollow block of clear acrylic just a couple of inches high. Compressed air is forced through this block, called an end sill, and out an array of tiny holes punctured in its top. This forms a curtain of bubbles in the water as it pours into the sand-filled streambed below. The idea is to soften the impact of the water, similar to an aerator in a kitchen faucet.

Barlock tested two types of acrylic end sills with five different patterns of holes and found that one configuration seems to do a better job of minimizing the scour hole. Identifying the best configuration is important, because running an air compressor big enough to aerate all the water flowing in a big still basin is expensive. “I also found that just having an endsill in place helped reduce scour,” she adds.

Barlock is planning to stay at Michigan Tech to pursue a master’s degree in civil engineering with a concentration in water resources. Growing up in the tiny Upper Michigan town of Bergland, she had no idea she would have this heady opportunity. “In high school, I was good in science and math, and my dad said I should be an engineer, but I didn’t even know what engineers did or what a master’s degree was when I came here,” she says. “I’m so excited to be doing this.”

Fantastic mathematics

by Marcia Goodrich

Kaylee Walsh

Kaylee Walsh loves all the branches of mathematics so much she can’t pick just one. “I can’t focus on one thing,” she says. “For me, that’s the beauty of math.”

Thus, she is completing her bachelor’s degree in mathematics with a concentration in general math, which, in a sense, is no concentration at all. But it does allow her to broadly indulge her joy in what Einstein called “the poetry of logical ideas.” Most recently, however, she focused on linear algebra as part of a research project with Mark Gockenbach, chair of the Department of Mathematical Sciences.

Walsh is acutely aware that most people wouldn’t have the vaguest understanding of what she does, and she takes pains to explain. “Linear algebra takes a system of equations and represents them as matrices or vectors,” she says. “So instead of addressing one equation at a time, you can address them all collectively.”

For the project, she and Gockenbach tried to develop a better way to de-blur images. To do this, they used a tool of linear algebra called Tikhonov regularization, applying methods recently developed by other researchers. “For example, if you take an MRI, sometimes you get a blurry image because there’s noise in your data,” Walsh says. It’s quite likely that you won’t ever be able to extract the perfect image from the noise, but using Tikhonov regularization narrows down the range of possibilities, so you can get a better result.

The project began last summer and was grueling, building matrices and proving they would work. “In math textbooks, you do proofs all the time, and it’s no big deal,” she says. “It was neat to have to do my own, to struggle the way the early mathematicians struggled. A lot of it was over my head, but some days, I just took it on faith.”

The struggle is paying off. The regularization method isn’t perfect yet—sometimes it overcorrected for noise, and sometimes it undercorrected—but Walsh and Gockenbach have made progress. They have coauthored a paper, and Gockenbach expects to build on their findings, probably with a graduate student.

It won’t be Walsh, at least for now. She has accepted a job offer from Gentex Corporation, in Zeeland, Michigan. “But it was so neat to go through this process, to find out what research is really like,” she says.

And besides, she adds, it was fun: “I love linear algebra.”

To find out about supporting student research, contact Vice President for Advancement Shea McGrew, smcgrew@mtu.edu, 906-487-3447.

Michigan Technological University is a public research university, home to more than 7,000 students from 54 countries. Founded in 1885, the University offers more than 120 undergraduate and graduate degree programs in science and technology, engineering, forestry, business and economics, health professions, humanities, mathematics, and social sciences. Our campus in Michigan’s Upper Peninsula overlooks the Keweenaw Waterway and is just a few miles from Lake Superior.