© Christopher Earls Brennen


``When dealing with water
First the experience
Then the theory.''

Leonardo da Vinci

Toward the end of my last spring as an undergraduate my tutor, Les Woods, casually enquired as to whether I might be thinking about continuing to work toward a higher degree. I think he had more confidence in my academic ability than I did, but, in any case, as a relatively new faculty member he was anxious to acquire some graduate students with whom he could conduct his research. I had been interviewing for industrial jobs with little enthusiasm and only modest success (I suspect that my Northern Irish accent was a significant handicap) and therefore my attraction to graduate work increased as the weeks wore on. Of course, that opportunity depended on success in the final examinations and I was not very confident in that regard. I was in the United States when the results were posted and so the first I knew of it was when I was congratulated by a fellow student who had heard through the grapevine that I had earned a first class honors degree. Anxious to have confirmation of this surprising news, I managed to make my way to the newspaper room of the Harvard Library where, in a recent copy of the London Times, I found the Oxford degree results and the desired confirmation. At that point, my immediate academic future was assured.

These developments had occurred so rapidly and had been compounded by so many other important matters (such as my marriage to Doreen) that I really had not given enough thought or attention to the details. For example, I had made very little effort to consider what area I might like to focus on for my graduate research. I had always been attracted to the subject of mechanics; indeed, even in high school, I had been fascinated by the Newtonian mechanics of objects like rockets, planets and billiard balls. Les Woods had specialized in fluid mechanics during the earlier part of his career and I had enjoyed my undergraduate studies of fluid flow. Therefore, I thought that fluid mechanics would be an appropriate choice though, in all honesty, the decision may simply have been the path of least resistance rather than a carefully considered plan. It would not be until years later that I recognized that some of the most remarkable mathematicians and physicists who had contributed to our fundamental understanding of fluid mechanics were Irish by birth. Among these were Robert Boyle (1627-1691), discoverer of Boyle's Law and the fundamental properties of gases and a founding fellow of the Royal Society, and William Rowan Hamilton (1805-1865), inventor of the characteristic functions of dynamics and the first foreign member of the US National Academy of Science. More pertinently, several of the greatest fluid mechanicists were Northern Irish. The man who, along with the French scientist, Navier, first constructed the basic equations governing the flow of a viscous fluid was George Gabriel Stokes (1819-1903), born in County Sligo. Every student of fluid mechanics soon becomes aware of the importance of the Navier-Stokes equations. Then there were the two great scientific sons of Belfast. William Thomson (Lord Kelvin) (1824-1907) first defined the absolute temperature scale and made major contributions to thermodynamics; his statue stood in the Botanic Gardens stood just across the street in Belfast from where I lived as a young child. If I had been able to read I would have learnt from the inscription that ``He elucidated the laws of nature and applied them to the welfare of mankind.'' The other great Belfast fluid mechanician was Osborne Reynolds (1842-1912) who made major contributions to the understanding of turbulent flows; his accomplishments are memorialized in the "Reynolds Number", a calculated quantity that allows one to determine some of the key characteristics of a fluid flow. I was born within a hundred yards of where Reynolds was born and so I used to tell my class that "I had a very low Reynolds Number". Which would imply that I moved very viscously; not very accurate methinks.

So it was that I launched into research in October of 1963. I began by attending advanced classes in mathematics, by studying several advanced fluid mechanics texts and by reading papers that Les Woods thought would interest me. Within the first couple of weeks I quite severely injured my left knee playing rugby and had to take time out to fly back to Northern Ireland in order to receive medical attention. Eventually however I resumed my classes and studies. I particularly remember the mathematics classes taught by Prof. George Temple, a kind man who was particularly concerned with my welfare following my injury. The fluid mechanics text that I started with was L.M.Milne-Thomson's "Theoretical Hydrodynamics", a book for which I never really cared. The first paper that Les Woods suggested I study in detail was a paper by Jack Kennedy on the formation of dunes and anti-dunes in hydraulic sediments, a paper which I did enjoy though it was hard to see what I could add to what Kennedy had done. Then toward the middle of the first year Les suggested I study papers on the subject of fully-developed cavity flows and thus began a lifetime of fascination and research into the subject of cavitation. Fully-developed cavity flows occur in a high speed flow past an object when the wake pressure falls below the vapor pressure and the wake fills with gas or vapor rather than liquid. This leads to spectacular flows with huge bubbles whose surface is sometimes frothy and sometimes glassy smooth. They are simultaneously spectacular and beautiful. Part of their attraction for me was aesthetic. Les had suggested that I might try to calculate theoretically the shape of these vapor-filled wakes or bubbles and that seemed to me a neat thing to try and do. Though some theoretical, mathematical predictions for the shapes of cavities existed for very simple, impractical objects, the only way forward for more practical objects would be to use numerical methods. This idea of using computers to predict these kinds of flows was then in its infancy (this is 1963); I had heard of those early efforts and was very interested in learning more. Consequently I dived into that project and began several years of what we would now call "code development", trying to develop calculational methods that would allow prediction of cavity flows. The project turned out to be more difficult than I first thought because the shape was very sensitive to small changes in the flow velocity. Thus the code became more and more complex and my need for time on the computer became greater and greater. When I began this work Oxford University owned only one very primitive computer, called a "Mercury Ferranti", housed in what was the surveying department. It operated with vaccuum tubes and tended to malfunction approximately once every half hour. The programs were prepared on 5-hole punched tape, identical to "ticker-tape"; indeed the tape readers and tape punchers were simply the devices used in the stock market. The programs were written in a computer language called "Auto-code" which was surprisingly similar to the modern "Basic" language. Due to the frequent breakdowns of the computer, the only practical way to make progress was to print out results every 15 minutes or so; in this way I could restart the calculation after each breakdown without having to go back to the start. Even without breakdowns the computer was very slow and hence I needed to spend large chunks of time on it in order to progress. Fortunately, I was able to persuade the Computer Department to teach me how to operate the computer and to spend one night per week doing my own calculations throughout the night when the normal operating staff were home in bed. Thus, for about a year, my working hours were almost completely time-shifted since, one night per week, I would spend from 7pm until 7am the next morning trying to pry useful results out of the Mercury Ferranti. There was one awkward aspect to this night-time activity, namely that the Department required me to have at least one other person present during the entire time I was operating the computer. Sometimes, I would be able to find another student with similar needs for extended computer time. But, on other occasions, Doreen and our infant daughter, Dana, would be kind enough to spend the night there with me.

After that first year, matters improved greatly for the University purchased a more advanced computer from English Electric called a KDF9. It was much faster, somewhat more reliable and used eight-hole paper tape rather than five-hole. However, it would not accept Autocode and so I had to rewrite my programs in a new programming language. We were all urged to learn and use "Algol", a cumbersome and awkward language that I did not like at all. Fortunately, an alternative rapidly became available, namely "Fortran" and I rapidly converted to and used that language which was not all that different from Autocode. I was to use Fortran and Basic (even more similar to Autocode) for most of the rest of my academic career. It was not long before I learnt how to operate the KDF9 and got permission to resume my night-long efforts to compute cavity flows. In the end, I had devised new computational methods and used them to produce a raft of calculated shapes for fully-developed cavities behind objects like discs and spheres.

But Les Woods rightly thought that I should also have some exposure to experimental methods during my doctoral studies. Not being an experimentalist himself, he made use of his contacts at the National Physical Laboratory (NPL) in London to arrange an introductory visit to that government laboratory in the outskirts of London. Parenthetically I should add that the drive from Oxford to London in Les's car was exciting for Les drove an automobile like you might expect a fighter pilot to drive. Nearing London, we encountered a series of roundabouts and Les's tactic when approaching these obstacles was to accelerate into the circulating traffic, scaring the hell out of the other drivers to say nothing of yours truly. Somehow we arrived unscathed at the Ship Division of the National Physical Laboratory in the London suburb of Feltham, just south of Heathrow Airport. There I met Les's acquaintances, Alec Silverleaf, George Gadd and John English, had an opportunity to explain to them my thesis research and to see the experimental facilities at the Laboratory. These facilities were particularly impressive. They included a 3/4 mile long towing tank in which ship models were tested and one of the largest water tunnels in the world that was to figure large in my later research. We also made arrangements for me to spend six weeks at the Laboratory the following summer. So it was that I stayed with a family in Feltham during June and July of 1966 and was allowed the opportunity to conduct research at the Ship Division under the guidance of George Gadd and John English. Several years before they had constructed a small blowdown water tunnel in order to demonstrate the phenomeon of cavitation at a trade show and thought that it might be valuable to more thoroughly investigate the cavitation in this device. To do this they arranged for me to use a high speed camera to take photographs of the fully developed cavities behind a disc for a range of operating conditions. While the limited time only allowed a very preliminary set of results, it laid the groundwork for the research I conducted at Ship Division after my PhD. I then returned to Oxford to resume work on the computations of fully developed cavitation.

Research equipment at Ship Divison, NPL.

After about three years as a graduate student, I began to prepare a PhD Thesis. In the end the thesis was about 400 pages long. Apart from its contents, I believe the way in which I produced it was quite novel for that time. I realized that I could type the thesis on the eight-hole paper tape machines used to prepare the programs for input to the KDF9. Then, by feeding the thesis tape into the computer I could get it to rapidly print out a copy of my thesis. This had several great advantages over the traditional production methods that other students used at the time to prepare their theses, namely by paying a typist to do it for them. First I could readily make corrections, cut and splice the corrected tape into the master tape and then print out a revised version. Second I could, with little difficulty, make as many copies as I wished (five official copies were required but at least double that number were needed). Thirdly, since no one kept track of the paper used, I could do all this for free. Since typist costs were substantial and Doreen and I had very little money this was a serious advantage. Fortunately, no one objected to the slightly odd font that the computer produced. After I received my PhD (or rather my D.Phil. for those are the initials Oxford preteniously prefers) I did not look at the thesis for many years, afraid to be reminded of what I thought was poor, beginner's writing. But when I eventually did examine it again, I have to say that I was favorably impressed not only with what I managed to accomplish but even with the writing that was not as bad as I feared it had been. Moreover, many decades later the work was used throughout the world (but particularly in the Soviet Union and in the USA) as a starting point for development of more advanced methods for calculating fully-developed cavity flows.

A few weeks before beginning the writing of my thesis we decided to terminate the lease on our cottage. Doreen and Dana flew back to Northern Ireland to stay with her parents so that I could devote my whole time to writing and thus complete the thesis as quickly as possible. For the next two weeks I did nothing but write, draw and type until the task was finished. I worked for about 22 hours each day, taking a surreptious one-hour nap each afternoon in the basement of my office building. Of course, the human body cannot keep up such a regimen for very long and I remember my thought processes beginning to disintegrate after about eight days. I also remember watching the sun come up while the computer ground out the printing and noting how just a few rays of sun had a remarkable, rejuvenating effect on my brain. Finally, the thesis was finished, bound and delivered to the appropriate Administrative Office of Oxford University and, much to my amusement, I was given a receipt written in Latin. After sleeping in a friend's spare bed for the best part of a day and a half, I flew back to Northern Ireland with some feeling of satisfaction.

So it was that seven marvellous years in Oxford came quietly to an end in the fall of 1967. I was a very different person than the boy that had timorously travelled to the plains around the Isis and the Cherwell seven years earlier. I had earned the highest degree in the land and rubbed shoulders with royalty. I had begun travelling the world and gained the confidence that I could hold my own in any company. On a personal level, I had married the first great love of my life and fathered my first child. I had begun to learn what mattered to me and what I most wanted to do with my life. I had acquired the wisdom to know what I believed and even the ability to recognize defects in the culture of Oxford. In particular, the attitude of many English toward the Irish left in me a recognition of the deeply debilitating effect that discrimination can have on an individual. Of course, many more lessons, positive and negative, were yet to come but much of what came later was made possible by those scintillating and emboldening years in Oxford.

Last updated 10/1/01.
Christopher E. Brennen