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  • Credit: EAS communications office
  • A doubly periodic Couette flow showing 28 Taylor cells stacked top to bottom, and five waves traveling horizontally per cell.
    Credit: Donald Coles, "Transition in circular Couette flow," Journal of Fluid Mechanics, 1965
  • Coles plotted the transitions from state to state in this 3-D graph. (The vertical axis, R, is proportional to the inner cylinder's rotation speed.) The topmost green arrowhead marks the 28/5 state shown in the previous image; the set of blue double-headed arrows traces a reversible sequence of transitions.
    Credit: Donald Coles, "Transition in circular Couette flow," Journal of Fluid Mechanics, 1965
  • Backlighting the waves makes the two sets easier to see.
    Credit: Donald Coles, "Transition in circular Couette flow," Journal of Fluid Mechanics, 1965
  • In this photo from the October, 1961 issue of Caltech's Engineering & Science magazine, then-research fellow and future aeronautics professor Brad Sturtevant (MS '56, PhD '60) fits a fresh diaphragm between the two sections of the 17-inch shock tube.
    Credit: James McClanahan
  • Ken Coles (BS '79, geology, MS '79, geology), poses for his senior yearbook photo with proud father Don in the latter's office.
    Credit: John Faughnan (BS '81)/Ken Coles/The Big T
05/06/2013 21:11:12

Donald Coles

1924 – 2013

Donald Earl Coles (MS '48, PhD '53), professor of aeronautics, emeritus, passed away on May 2 at age 89. Coles was a master instrument builder famed for his ingeniously designed and precisely executed experiments. His doctoral dissertation provided the first comprehensive set of data on supersonic boundary layers. A few years later, he made an important addition to the theory of turbulent boundary layers that he christened "the law of the wake."

Coles was born on February 8, 1924, in St. Paul, Minnesota. His father, Courtney, was a streetcar driver, and his mother, Lorna, was a teacher. "I think she taught him his work ethic, and the value of education," says his son Kenneth (BS, MS '79), an associate professor of geoscience at the Indiana University of Pennsylvania. "Like any kid of his generation, he grew up dying to fly." A meticulous craftsman even in adolescence, Coles built exquisite airplane models from balsa wood and tissue paper and traded them to local pilots in exchange for flying lessons. He soloed at 16 and got his pilot's license before he learned to drive, Ken says. In his senior year of high school, his model-building prowess won him an engineering scholarship to the Boeing School of Aeronautics in Oakland, California. However, his path to a degree would itself encounter considerable turbulence.

Coles entered the Boeing School in 1941. The following year, it was pressed into service for military training. Civilian students had to leave, so Coles hired on as a detail draftsman with the Lockheed Aircraft Corporation in Burbank. When the draft age was lowered to 18 he entered the Army, and eventually "he signed up as a combat engineer, because he heard that they would send you to college," says Ken. "His whole mission in life was to get a college education."

The Army put Coles through a six-month crash course at the University of Michigan before sending him overseas in early 1944. According to Ken, "He got appendicitis just in time to not go in with his unit [the 291st Engineer Combat Battalion], which wound up having to shoot its way out of the Battle of the Bulge." However, he did catch up with the 291st in time to help build a tank-worthy pontoon bridge across the Rhine River at Remagen, allowing the Allies to enter the German heartland. The bridge, more than 1,100 feet long, was built in only 32 hours despite fierce opposition—including being "on the receiving end of a couple of V-2s," Ken says.

Coles finally earned his bachelors degree in aeronautical engineering from the University of Minnesota in 1947, acquiring an aircraft engine mechanic's license that same year. He also married Ellen Searight, an editor at the University of Minnesota Press. By then part owner of a Cessna, Coles "courted my mom in the airplane," says Ken, adding that they once got lost over the endless fields of Wisconsin—on the trip to meet her folks. "He flew on until he found a railroad line, then turned and followed the tracks until he came to a water tower with the name of the town painted on it."

Minnesota aeronautics professor Jean Piccard urged Coles to "do something with himself" and apply to graduate school at Caltech, Ken says. (The Swiss-born Piccard twins were Star Trek creator Gene Roddenberry's inspiration for Captain Jean-Luc Picard; Jean was a pioneering high-altitude balloonist, while his brother Auguste invented the bathyscaphe—a sort of underwater zeppelin used for deep-ocean diving.) The newlyweds drove cross-country to Pasadena that summer, and Coles joined aeronautics professor Hans Liepmann's research group at the then Guggenheim Aeronautical Laboratory at the California Institute of Technology (GALCIT).

In his final three years as a grad student, Coles also worked full-time as a senior research engineer at Caltech's Jet Propulsion Lab. He used JPL's supersonic wind tunnel for his doctoral research, collecting data on turbulence in the so-called boundary layer at flow speeds ranging up to four and a half times the speed of sound.

Whenever a fluid flows past a solid—be it air over a wing, or oil in a pipeline—the molecules adjoining the surface tend to stick to it. Thus the flow velocity right at the wall is zero. How fast the flow increases as you begin to move away from the wall depends on the fluid's viscosity. This region is called the sublayer, and the flow within it smoothly follows the wall's contours. The boundary layer, where turbulence reigns, lies just beyond the sublayer. "Turbulence flowing along a surface is very complicated," Coles remarked in a recent interview, "because the surface changes the character of the turbulence. A large fraction of the field deals with this subject." Even so, a universal theory of turbulence remains elusive. "There is no theory," Coles said. "There is no truth about turbulence except experimental truth."

Coles drily pointed this out in his PhD thesis, which begins, "A contemporary Texan, J. Frank Dobbs, has said in another context that research is frequently a process of moving old bones from one graveyard to another. Those who have tried to find their way recently in the formidable literature of boundary layers may agree that the metaphor is apt enough." Coles's dissertation won the 1953 Lawrence Sperry Award from the Institute of the Aeronautical Sciences (now the American Institute of Aeronautics and Astronautics) "for fundamental contributions to the understanding of supersonic skin friction."

Absent a grand unified theory, fluid mechanics relies on experimentally derived equations called "similarity laws." The first of these, the law of the wall, stems from work done at the turn of the 20th century by Ludwig Prandtl at the University of Göttingen and was published in 1930 by his student Theodore von Kármán, GALCIT's founding director. "The law of the wall says that the flow velocity in the boundary layer varies logarithmically with distance from the sublayer outward," Coles explained with a chuckle. "That logarithm has exercised a lot of people. There is no widely accepted theory that lets you derive it. It's just there. You do an experiment, and there it is. "

In 1954, Francis Clauser (BS '34, MS '35, PhD '37), then at Johns Hopkins University, developed a fluid-mechanic equivalent of a lab rat—a special class of easily reproducible flows whose parameters greatly simplified point-by-point calculations within them. Said Coles, "As a postdoc, I looked at Clauser's flows and proposed a new similarity law, which I called the law of the wake." The law of the wake applies where the law of the wall leaves off. As a flow proceeds downstream, its boundary layer expands in a wedge like the wake of a passing speedboat. Within this wedge, fluid from beyond the boundary layer mixes into the flow in large, turbulent swirls. Here the flow rate at any point no longer depends on its distance from the wall, but on the distribution of angular momentum among the eddies. The resulting paper, titled "The law of the wake in the turbulent boundary layer," was published in the very first volume of the Journal of Fluid Mechanics in 1956.

Coles then turned his attention to a "lab rat" of his own—the Couette flow. Introduced in the late 1800s by French physicist Maurice Marie Alfred Couette, the apparatus consists of two concentric, independently rotating vertical cylinders. Setting one or both of them in motion causes the fluid filling the narrow space between them to circulate round and round. Couette flows are now widely used to study the transition between steady and turbulent flows in pipes and channels.

An elegant theoretical analysis of Couette flows had been published by Sir Geoffrey Taylor in 1923, says Anatol Roshko (MS '47, PhD '52), the Theodore von Kármán Professor of Aeronautics, Emeritus, and "Don built a very beautiful experiment to look into that further. Very well thought out and executed." Coles's version consisted of two eight-inch-tall concentric cylinders made of carefully polished glass. The half-inch gap between them contained clear oil in which tiny aluminum flecks were suspended. A lightbulb inside the cylinders illuminated the flecks so that their motions could be recorded. The flecks would arrange themselves into an impressive variety of patterns that depended on the two cylinders' speeds and their relative directions of rotation, but one set of patterns held a particular fascination.

When the outer cylinder was locked down and the inner one gradually spun faster and faster, paired sets of parallel bright and dark bands would suddenly fill the cylinder from top to bottom. Each pair of bands represented the top of a convection cell—the fluid near the spinning inner cylinder was flung outward by centrifugal force; meanwhile, the outermost fluid would drift inward, slowed down by the drag exerted on it by the stationary outer cylinder. The situation is similar to the large convective cells of hot air rising and cold air sinking that drive our planet's weather systems; in fact, both are called Taylor cells. As the inner cylinder's speed slowly increased, the bands began to undulate in waves traveling in the same direction at about one-third of the cylinder's speed. Then, as the cylinder revved ever faster, a second set of independent waves would suddenly burst into being, superimposing itself on the first set. This "doubly periodic flow," Coles would later write, had "a fascinating peculiarity"—"the flow pattern was observed to change abruptly, discontinuously, and irreversibly from one state to another at certain well defined and repeatable critical speeds."

Each state consisted of a specific number of Taylor cells undulating an integral number of times around the apparatus's circumference. While the number of cells and the number of waves in each state could be predicted from Taylor's equations, the transitions from one state to another could not. Coles cataloged 74 distinct transitions, and by plotting the order in which they occurred, he discovered that "at any specified speed . . . there exists a variety of possible operating states, sometimes more than 20 in number, among which the one actually observed is determined by the whole previous history of the experiment." Subtle differences in initial conditions could produce markedly different results, yet every pathway was repeatable. Coles summarized a decade's worth of work on Couette flows in a 40-page, lavishly illustrated paper that appeared in the Journal of Fluid Mechanics in 1965. The paper, which continues to be cited more than 1,000 times a year, has led to advances in the mathematics of group theory as well as in fluid mechanics.

Coles designed several of GALCIT's experimental facilities, including the 17-inch-diameter shock tube—in essence, a giant cannon. Built in the early years of the Space Age to study the shock waves encountered by ballistic missiles and space capsules as they reentered Earth's atmosphere, the tube was designed to operate at very low pressures—an unconventional approach that researchers to put the shock waves under a magnifying glass, as it were. At normal atmospheric pressures, a shock wave is a few millionths of an inch thick. The shock waves broaden as the air gets thinner, until, at a pressure equivalent to an altitude of roughly 60 miles, they become about half an inch thick—enough to make precision measurements of their internal structure. The tube's unusually large diameter and its precision-machined, mirror-smooth interior were designed to minimize any distortions to the shock wave from the tube itself, which is made of stainless-steel pipe half an inch thick.

The shock tube is divided into two unequal lengths by a metal diaphragm. The tube's "driver" section is filled with an inert gas, and pressurized until the eighth-inch-thick aluminum sheet bulges into the "test" section like a balloon. The diaphragm presses up against an X-shaped set of knife edges and eventually ruptures; the pent-up gas behind it blasts into the test section, creating a shock wave that travels at up to eight times the speed of sound.

Coles introduced several innovations that are now standard practice. For example, "there's a flange on the low-pressure side, a flange on the high-pressure side, and the diaphragm in the middle," Roshko explains. "Shock tubes used to be built with a dozen or more bolts that you put through the flanges and tightened, but he designed a clamp that went around the whole thing. You just grab the flanges with a great big caliper, and a wedge inside squeezes them together." Swapping the broken diaphragm for a new one takes about 30 seconds, greatly reducing the time between shots, and the whole facility can be run by a single person.

The tube is 80 feet long, or about half the length of Guggenheim itself. It runs straight down what was the middle of Liepmann's third-floor lab, suspended overhead from a track bolted to the ceiling. This absorbs the recoil and allows the tube to be opened easily while keeping the floor clear for other important apparatus, including the Ping-Pong table "used for unsponsored research in low-speed aerodynamics." The initial studies were wrapped by the end of the 1960s, and the shock tube "has been used for many things since then," Roshko says. "It's been very useful, because it's so easy to operate."

Coles inculcated his innovative style into generations of GALCIT's grad students via a course called Ae 104, Experimental Methods. Says Roshko, "He tackled some really sophisticated experiments," posing a question and setting the students to design and build the apparatus needed to answer it. "It couldn't be something very large scale, as it had to be built within the quarter and some results obtained," Roshko observes. Coming up with a research problem challenging enough to be worthwhile, yet doable in the allotted time takes a real knack, but "he was very good at getting that done. And in a few cases, they developed into thesis topics."

In Ae 104, with his own grad students, and to his fellow faculty members, says Roshko, Coles's "innovations and detailed designs were very helpful. He was completely devoted to Caltech, and to GALCIT, and to a life of research. And that's important, because he himself was kind of daunting. It wasn't shyness, just a deep reservedness. Once he accepted you, he was incredibly generous with his time."

Coles's legendary perfectionism set the standard around GALCIT. "It pained him to see anything not done absolutely as well as it could possibly be done," Roshko says. "When I added an innovation to the 17-inch shock tube that saved a lot of machining, he was impressed, and he told me. That made me feel really good, coming from him—much more so than it would have, had it come from somebody else."

Coles retired in 1996 and began writing a definitive work on turbulent shear flow, based on the course notes and data he'd compiled over his career. The book, which was very nearly finished at the time of his death, will be published posthumously.

Coles was a member of the National Academy of Engineering, and a fellow of the American Institute of Aeronautics and Astronautics (AIAA), the American Physical Society (APS), and the American Association for the Advancement of Science. He received the AIAA's 1985 Hugh L. Dryden Medal and the APS's 1996 Otto Laporte Award for his body of work. In 2000, the Donald Coles Prize in Aeronautics was established; it is awarded at Commencement to the aero PhD "whose thesis displays the best design of an experiment or the best design for a piece of experimental equipment." And in 2011, GALCIT created the Donald Coles Lectureship in Aerospace in his honor.

Coles is survived by his wife, Ellen; by his four children, Christopher, Elizabeth, Kenneth, and Janet; by his sister, Marjorie Schlaegel; and by two grandchildren.

Plans for a memorial service will be announced at a later date. 

Written by Douglas Smith