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The following negotiations lasted for over a decade and were interrupted by World War I. Ludwig Prandtl was appointed head of the institute. Before, in the application-oriented Aerodynamical Experimental Station had been founded at the same location. The wind tunnel that Prandtl had built in the Hildebrandt Street was moved to the Bunsen Street in On April 11 th , the British military government temporarily closed the Kaiser-Wilhelm-Institute and the Aerodynamical Experimental Station and installed a committee to decide about the future of both research facilities.

In June a decision was made: The Aerodynamical Experimental Station was permanently closed and its experiments were dissembled. Having been built for the purpose of fundamental research only, the Kaiser Wilhelm Institute was permitted to carry on its work and was reopened on August 1 st , In the same year Ludwig Prandtl resigned as head of the institute.

Also in the Max Planck Institute began to focus on new fields of research and received three departments for molecular physics: Atomic and Molecular Physics, Molecular Interactions and Reaction Kinetics. In the following years this field of research became more and more important until in the institute discontinued all research in fluid dynamics. In the institute again chose a new research focus and appointed Prof. Theo Geisel, who opened the Department of Nonlinear Dynamics.

By all departments dealing with molecular physics had been closed. With the appointment of Prof. Stephan Herminghaus and Prof. Eberhard Bodenschatz in and the founding of the Department of Dynamics of Complex Fluids and the Department of Hydrodynamics, Pattern Formation and Nanonbiocomplexity fluid dynamics returned to the institute.

However, now this field of research was put into the larger context of self-organized and nonlinear phenomena. This development led to the renaming of the institute on November 19th In September Prof. Geisel became Emeritus and is operating his department Nonlinear Dynamics as an Emeritus gruop. Im March Prof. Although influenced by editorial comment in some cases, the opinions expressed remain those of the authors themselves, and we, as editors of the volume, are deeply grateful to them all for the care and eort that they have devoted to their task. We hope that this volume, incomplete though it may be, will give a balanced perspective of the development of ideas and research in turbulence over what was in many ways an exceedingly turbulent century!

We wish to express our warm thanks to the Director and the sta of the Institute for their unfailing encouragement and support, and for providing an ideal environment for the initiation of a project of this kind. At the suggestion of Konrad Bajer, this conference will be followed by a symposium Turbulence the Historical Perspective, based on the chapters of this volume.

We wish to thank Konrad for taking this. Finally, we wish to thank David Tranah of Cambridge University Press, who has taken a close personal interest in the work, and has steered it from initial conception all the way through to final publication; without his guidance and encouragement, we would not have been able to bring the project to completion.

Peter A. More recent reviews have been provided by Gibson , a student of Reynolds and later an academic colleague, by Allen , who provided the opening article in a volume marking the passage of years from Reynolds taking up his chair appointment at Manchester in , and by Jackson , in an issue of Proc. A significant portion of the present account is therefore devoted to Reynolds family and background and to hitherto unreported aspects of his character to enable his contributions as a scientist and engineer to be viewed in the context of his life as a whole.

While inevitably some of what is presented here on his academic work will be known to those who have read the articles cited above, archive material held by the University of Manchester and The Royal Society and other material brought to light in the writers personal enquiries provide new perspectives on parts of his career. Starting in , three consecutive rectors of the parish of Debach-with-Boulge came from the Reynolds family. The Rev. Robert Reynolds was instituted on 6 September on his own petition. When he retired in September his son, the Rev.

Osborne Shribb Reynolds, became Rector. Then, on his death in December , his eldest son, the Rev. Osborne Reynolds, took over for a while. This last named, father of the main subject of this chapter, entered Cambridge University in as a fee-paying pensioner. After matriculating from Trinity College in , he transferred to Queens College from whence he graduated in as 13th Wrangler Venn, At that point it seemed that he was destined to follow a clerical career like his father and grandfather before him for he was ordained a deacon in Ely Cathedral the following year and became a priest a year later.

Their first child, Jane, was born in and, soon afterwards, they moved to Ireland where the Rev. Their second child, Osborne, was born on 23 August Crisp, It seems, however, that the Rev. Reynolds still saw a career in the church as his goal for in he returned to England with his family to take up an appointment as curate at the parish church in Chesham, Buckinghamshire.

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However, his tenure of this post proved to be short-lived. On February 6th, , his wife died as a result of complications following the birth, three weeks earlier, of their second son Edward The Times, 12 February , leaving the Rev. Reynolds with the responsibility of bringing up his three small children alone. That task, allied with the financial limitations of his post as curate at Chesham, provided the incentive for him to seek an alternative position. Reynolds took up his post at the end of and held it for almost eight years Jones, Besides carrying out his duties as headmaster he provided the personal tuition of his children, who lived with him at Dedham Census of Great Britain.

It seems that he was also working on inventions, for while in post he took out the first two of the six patents that would be registered in his name Ramsey, In fact, the small market town of Dedham is located only some 25 miles south-west of Debach. This relative proximity meant that the Rev. Reynolds was able to keep very much in touch with his father, the Rev. Osborne Shribb. Reynolds, and with the familys farming interests in Debach White, On visits there he occupied a farmhouse on the family estate. Moreover, when his father died in post in , the Rev.

Osborne Reynolds was able to take over as rector, which he did on his own petition White, , while remaining headmaster of Dedham Grammar School Clergy List, , p. This arrangement lasted until May when a replacement was appointed rector by the Church of England Crockfords Clerical Directory, Family misfortune still seemed to stalk the Rev.

Reynolds, for the following year his ten-year-old daughter, Jane, died at Dedham. In , having inherited much of the land and property in Debach, he resigned as headmaster at Dedham Grammar School or was persuaded to resign, as one contemporary account Jones, seems to imply to take on what amounted to the life of a gentleman farmer, managing the family estate in Debach which then employed some 30 sta Census of Great Britain. He lived at Debach House with his two sons whom he continued to educate, concentrating, it seems, on mathematics and mechanics.

As will be seen later, his elder son Osborne warmly acknowledged his fathers role in stimulating his own interest in mechanics. By the time of the next census his sons had both gone up to Cambridge University leaving Osborne Reynolds Senior free to concentrate on managing his estate and farming interests which, apparently, continued to flourish. Later, however, in the agricultural depression of , it appears that Osborne Reynolds Senior encountered financial difficulties.

In , at the age of 66, he relinquished the estate to take up the post of rector of Rockland St Mary in Norfolk a placement arranged under the auspices of his Cambridge College, Queens Crockfords Clerical Directory, , p. He finally retired in and moved to Clipston, Northamptonshire, where his younger son, Edward, was then rector Crockfords Clerical Directory, , p.

In summary, the talented but ill-fated Rev. Reynolds had an exceptionally strong influence on the formation and development of his elder son, Osborne Reynolds, who forms the subject of the remainder of this article. Not only was he directly responsible for Osbornes primary and secondary education but he stimulated in him a fascination for mechanics that was to be the bedrock of his lifes work. He went on to play a major role in shaping the path and covering the not inconsiderable cost of the further five years which his son spent receiving practical training in mechanical engineering and a university education in mathematics which were so pivotal to his subsequent career.

Moreover, the manner in which the Rev. Reynolds coped with the serious domestic misfortunes he faced must have provided a source of inspiration for his son. Osborne when strangely parallel developments later threatened to derail his own life. Reynolds was briefly Principal of the Collegiate School.

Despite the brevity of the familys stay there, numerous Irish history websites include Osborne Reynolds in their listings of famous Irishmen, lists that also include Sir George Stokes and Lord Kelvin, the former of whom plays a significant role later in this account. At the age of 19, having acquired from his father not just his schooling but also a fascination for mechanics, Osborne Reynolds entered the engineering workshop of Edward Hayes of Stony Stratford, a well-known trainer and teacher of mechanical engineers.

There, typically, a dozen privileged apprentices or, more transparently, since fees of up to per annum were charged, the sons of wealthy families would be taking their first steps in learning the rudiments of engineering manufacture, management and science The Engineer, 14 September , p. The nature of the training is well brought out by the following: The pupils. Whilst at the Works they had to conform to all the general rules and hours worked by the labour force. Most evenings were also spent with Edward Hayes being instructed in the technicalities of drawing, planning and estimating.

Other subjects taught were mathematics, mechanics and natural philosophy. The pupils received. Reynolds object in taking this placement, as explained later in a testimonial provided by Mr Hayes, was to learn in the shortest time possible how work should be done and, as far as time would admit, to be made a working Mechanic before going to Cambridge to work for Honours University of Manchester Archive. Indeed, in Osborne Reynolds was duly admitted as a pensioner to Queens College at the comparatively late age of 21 to read mathematics too old to be eligible for the recently established entrance scholarships.

Moreover, his fathers tuition had failed to include instruction in classical Greek on which, to his annoyance, he thus had to devote many hours. On passing the requisite examination early in his second year he ceremonially demonstrated his firmness of spirit by burning all his Greek textbooks despite the pleas of his friend and fellow undergraduate at Queens, Arthur Wright, who was studying classics, to pass them on to him Wright, In his specialist subject of mathematics Osborne Reynolds also viewed his experience at Cambridge with some disappointment.

Those who did attempt such a course found that they had spent several years in learning that which they had to lay aside on commencing their new work. Mathematics and the theory of mechanics, it is true, were then as now, the educational base most wanted; but these taught with a view to their application to the simpler problems of astronomy. However, this level of distinction did not come easily to him, as a quotation from one of his tutors will show.

Within a few months, news reached him that Owens College, Manchester, had advertised the creation of a Chair in Civil and Mechanical Engineering. On January 18th, he duly wrote a letter of application University of Manchester Archive that began: Gentlemen, I beg leave to oer myself as a candidate for the Professorship of Engineering at Owens [sic] College. I am in my twenty-sixth year. From my earliest recollection I have had an irresistible liking for mechanics; and the studies to which I have especially devoted my time are mechanics and the physical laws on which mechanics as a science are based.

In my boyhood I had the constant guidance of my father, also a lover of mechanics and a man of no mean achievement in mathematics and their application to physics. Much has been made of Reynolds youth and thus his. Figure 1. Reproduced with permission of the University of Manchester. However, Reynolds was by no means the youngest candidate: seven of the 16 were in their twenties, four of whom were younger than Reynolds.

In the s, a sound knowledge of mechanics and a vision of where it might lead in engineering applications must have been qualities predominantly possessed by younger candidates, much as knowledge and competency in certain aspects of software engineering are today. Unwin must have felt that he had a good chance, having been assured of very strong support from his former employer and mentor, William Fairbairn, FRS Allen, , who was chairman of the committee of industrialists in Manchester which had raised the money to fund the Chair. The College set up an appointing committee made up of trustees of Owens College and a selection of professors.

Fairbairn was not on that committee but, evidently, he must have been influential behind the scenes in guiding it with a view to ensuring that a suitable appointment was made. The procedure was for candidates to submit supporting testimonials and, in Reynolds case, at least, the handwritten versions of which there were 14 were complemented by a printed version of the same and of his letter of application itself University of Manchester Archive.

The testimonials included one from Mr Hayes from which the quotation above was taken, another from Archibald Sandeman, then Professor of Mathematics at Owens College but who had formerly been Reynolds tutor at Queens College, plus four others from Cambridge sta including one from James Clerk Maxwell, FRS, confirming Reynolds standing in the graduation list and ending with the important observation that I had to examine Mr.

Reynolds papers for the Mathematical Tripos, including his solutions of many questions in mechanics and general physics; and found that he had knowledge of sound principles which will enable him in the study and teaching of engineering to exemplify the practical use of sound theoretical principles, and to show that all his practical rules are founded on general laws established by experiment. Another referee, the Rev. Reynolds is an accomplished Mathematician. But he is not a mere theorist. He possesses a considerable acquaintance with practical mechanics and engineering.

For more than a year before he came to the University he studied the practice of the profession under Mr. Hayes of Stoney Stratford; and since taking his degree he has been occupied in like manner with Mr. Lawson of London. It would be dicult to find a Mathematician who combines such practical experience with theoretical knowledge. Fulsome communications were also received from J. Challis, FRS, Professor of Astronomy, and the mathematics tutor, John Dunn, who commented that while on entry Reynolds had lacked knowledge in mathematics, by innate talent and undeviating perseverance Mr Reynolds made the most rapid progress.

Perhaps most surprisingly to a 21st-century reader, his father, the Reverend Osborne Reynolds, also provided a testimonial at the suggestion of another referee , a task which, in his words, had surprised and embarrassed him. But this is compensated for by his early devotion to Science and the practice of his profession. Despite the considerable number of applications, the minutes of a meeting of the Owens Committee of Trustees on 30 January reported reservations on the part of the appointing committee about the response to the advertisement.

Accordingly, Mr Charles F. Beyer, a German who had come to Manchester as an impecunious young man to make his fortune and had certainly done so! It is more than likely that this decision was influenced by the following sarcastic article which had appeared in the professional journal, Engineering, earlier that month 10 January : Technical Education For all those who are interested in that subject of paramount national importance, upon which the future greatness of this country and its position in the civilised world are now recognised to depend for all those who are speaking, and writing, and working for the spread of technical education in this country we have gratifying news.

The trustees of Owens College, in Manchester, are advertising for an able-bodied man-servant to act as performing professor of engineering for the rising generation in the metropolis of Manchester, at the liberal rate of wages of thirteen shillings and eight pence per day. What a stir this grand opening will create in the scientific world! The greatest men of Great George street will close their oces and compete with each other; M. Flachat, Professor Conche, Baron Burg, and Professor Ruhlmann will leave their respective countries and professors chairs; men like Rankine, Scott Russell, and Clausius will gather in long processions in the streets of Manchester, and vie with each other to answer the call in the newspapers.

Thirteen and eight pence and a proportion of the fees paid by students and perhaps the free loan of a sewing machine for the professors wife to earn a little extra are worth applying for in a country where the income of the head master at Eton is estimated at , and that of an assistant master at the same school ranges from to a year.

In any event, a further 11 applications were received in response to the readvertisement with its upgraded salary, and there had also clearly been discreet contact with Professor William Maquorn Rankine, FRS, at the University of Glasgow who, after initially showing some interest in the post, chose not to. Both interviewees were drawn from the original list of applicants. Thus, with Rankine having eventually declined to become a candidate, the increased oer had served nothing other than to double the salary of the successful applicant.

As the world of fluid mechanics gives thanks, the chosen candidate was Osborne Reynolds, a decision which has been described by Smith as an inspired choice and one of the most successful gambles ever made by an appointing committee. A photograph of part of the formal terms of appointment is reproduced in Figure 1. As for W. Unwin, as soon as the Trustees decision had been reached, his former employer wrote to him Walker, : My dear Unwin, I am very sorry I cannot forward to you the agreeable intelligence that you are elected to the position of professor.

I so earnestly wished for you to occupy that position. It would have exactly suited your tastes, and I had every reason to believe you would have been an active and excellent professor. In wishing you better luck in your next undertaking, I am, Yours, Wm. The commissioned biography of Unwin Walker, , as works of that kind inevitably are, was staunchly supportive of its subject.

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Ignoring the fact that Unwin was not one of those invited for interview, it nevertheless chose to present the chair appointment as a contest between Unwin and Reynolds that involved at least misjudgement by the interviewing committee and perhaps political intrigue to boot: Bearing in mind the researches on materials and on bridge design which he at that time had recently completed. Owens [sic] College at that date was, to a very great extent, a municipal undertaking and one cannot help thinking that, in the lively atmosphere that surrounded its early development, considerations other than academic may have played some part in the deliberations of the Senate.

It is noted for the record that none of the documents seen in the University of Manchesters archives lends any support to Walkers insinuation that considerations other than academic may have played some part in the decision. Moreover, few if any would agree with Walkers suggestion that Reynolds subsequent fame. As Reynolds pioneering contributions have abundantly made clear, however, engineering breakthroughs habitually require a mind possessing deep physical insight! In this lecture, entitled The progress of engineering with respect to the social conditions of this country, he firmly rejected any notion of engineering as an ivory tower abstraction divorced from human context: The results, however, of the labour and invention of this century are not to be found in a network of railways, in superb bridges, in enormous guns, or in instantaneous communication.

We must compare the social state of the inhabitants of the country with what it was. The change is apparent enough. The population is double what it was a century back; the people are better fed and better housed, and comforts and even luxuries that were only within the reach of the wealthy can now be obtained by all classes alike. But with these advantages there are some drawbacks. These have in many cases assumed national importance, and it has become the province of the engineer to provide a remedy. These remarks made at the outset of his career show the youthful Reynolds, whose contemporary portrait photograph appears in Figure 1.

Here was a figure charged with a sense of mission, full of ideas and ready to face the challenges ahead of him in serving the needs of society as Professor of Engineering at Owens College, Manchester. However, the associated joy was short-lived for, after delivering their first-born child also named Osborne on 15 July , Charlotte died 12 days later The Times, 29 July , leaving Reynolds with the.

The cause of death, a peritonal infection, was noted on 31 July in an article in The Lancet on Dr Chadwick and his bereavement. Clearly, these personal events posed a dicult beginning for Reynolds, even knowing that his father had managed to cope with a similarly challenging start to his own career. Fortunately, Reynolds salary from Owens College was sucient for him to be able to employ live-in domestic help to assist in running the household and caring for his son Census of Great Britain. He read his first paper to the society in March on The stability of a ball above a jet of water an interesting though rather academic fluid-dynamics problem.

This marked the beginning of a close involvement on Reynolds part with the Lit. These were mainly on scientific topics of general interest and broad appeal. In a bid to further extend both his own and the Colleges contacts with the technical and industrial community of the area, Reynolds also actively involved himself with two other local societies, the Manchester Association of Employers, Foremen and Draughtsmen a group consisting of men with technical expertise and experience, first formed in and the Manchester Scientific and Mechanical Society formed in by William Fairbairn with the intention of linking academics with local industrialists.

Between and Reynolds addressed the first of these bodies on a number of directly practical topics: Elasticity and fracture; The use of high pressure steam; and Some properties of steel as a material for construction. In contrast, his lectures to the Scientific and Mechanical Society, which he twice served as President, were of a more general nature, as indicated by titles such as Future progress, Engineers as a profession and Mechanical advances.

In these ways, Osborne Reynolds set out to address the specific needs of the rather diverse sectors of his local social and technical constituency. At the time of Reynolds appointment Owens College which had been founded in following a generous bequest by John Owens occupied a building on Quay Street, an early photograph of which appears as Figure 1.

The building, now restored, is today used as chambers for barristers. In the newly formed Engineering Department was accommodated in what had been the stables at the rear of the building. In his recollections, Thomson who had grown up in Cheetham Hill, Manchester, and enrolled as an engineering student in at the age of 14 noted that the stable itself was converted into a lecture room and the hayloft above it into a drawing oce.

Little was available in the way of facilities and equipment for experimental work and Reynolds had to rely on using other science laboratories in the College or performing simple experiments at home. This situation explains why his very early papers were concerned largely with explaining natural phenomena, what Thomson later termed out-of-door physics. The work falling under this heading has been summarized in Jackson while the papers themselves all appear in Volume I of Reynolds Collected Works Reynolds, The tails of comets, the solar corona and the aurora, followed by the inductive role of the Sun on terrestrial magnetism, the electrical properties of clouds and the phenomenon of thunderstorms form some of the subjects of the early papers in this group.

A further paper concerned the bursting of trees struck by lightning, the cause of which Reynolds was able to link to the rapid vaporization of moisture within a tree trunk by the sudden discharge of electricity through it. There were other papers on the destruction of sound by fog and the refraction of sound by the atmosphere.

Thereafter, he tackled topics such as the. For some of these studies he contrived simple but eective small-scale experiments using relatively unsophisticated apparatus. Even after the removal of the College in to a new purposebuilt campus on a site south of the city centre today the core of Manchester University there was initially only limited scope for experimental work. A fuller summary of this phase of Reynolds research appears in Jackson together with reproductions of the diagrams of the apparatus used in each case.

Lamb records in his obituary notice that for some time after Reynolds arrival, while he was concentrating on these out-of-door physics problems. This happened despite the fact, noted above, that Reynolds was at that time actively integrating with the societies that served local manufacturing and industrial management needs.

Of course, some delay in getting started on engineering research was inevitable but, as soon as it was practicable, Reynolds did begin to address a whole range of problems of a more practical nature, beginning with two experimental papers on heat transfer, one considering the eect of the presence of air in steam on the condensation rate at a cooled surface Reynolds, and the other on the extent and action of the heating surface of steam boilers Reynolds, In the latter he proposed and demonstrated links between pressure drop and the rate of heat transfer, establishing an analogy between the diusion by means of turbulence of momentum and thermal energy.

These studies accompanied others concerned with the eciency of belt drives as communicators of work and the phenomenon of rolling friction. At about that time Reynolds also initiated some work on the racing of ships screw propellers and also on the multi-staging of turbines and centrifugal pumps, the latter leading in to a detailed patent specification. Regarding this work, Gibson has pointed out that it anticipated the multi-stage Parsons turbine. Later, Reynolds went on to produce a series of important reports for the British Association for the Advancement of Science concerning the eect of propellers on the steering qualities of ships.

Again, all the work referred to above is summarised in Jackson and the papers can be found in Reynolds In the second half of the s Reynolds research in fluid mechanics underwent a shift towards more general phenomena such as the progression of dispersive surface waves in deep water and the motion of vortices, the latter made visible by coloured dye traces in water.

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He also made fundamental contributions in physical science concerned with forces caused by the communication of heat between a surface and a gas, explaining the operation of the Crookes light mill and constructing the experiment by means of which his ideas on this were validated. These provided valuable confirmation of the kinetic-theory model of gaseous fluids.

He went on later to apply such theory to the phenomenon of thermal transpiration of gas through a porous medium Reynolds, , accompanying this with experimental work to validate his ideas. A fuller discussion of these aspects of Reynolds work can again be found in Jackson see also Allen, and Jackson, In recognition of the wide-ranging contributions to both engineering and science which Osborne Reynolds had made within the decade following his appointment, he was admitted in to Fellowship of the Royal Society of London. Throughout this very busy and productive period of his career at Owens College, Reynolds remained a devoted and involved father, as is well illustrated by a letter Reynolds Society Archive Ref.

RS RR. The letter mainly concerned referees comments on the manuscript of his paper On certain dimensional properties of matter in the gaseous state Jackson, , but he also commented: I am here nursing my only child who is very ill and I do not like leaving him even for a day or I would try to see you and save you some of this writing.

I expect to be here all the Summer. In fact, despite this love and attention, Reynolds son died on 27 September while they were still at St Leonards-on-Sea. Yorkshire Post, 30 September This personal tragedy that again, curiously, paralleled events in his own fathers life, may be said to mark the end of the first phase of Osborne Reynolds professorial career.

Henry Wilkinson, Rector of Otley in Suolk. No account is available of how the couple met but it is not all surprising that they did because Otley was the parish next to Debach-with-Boulge where, as already noted, his father had continued to live until after relinquishing the headmastership of Dedham Grammar School. The wedding took place in Otley church with the bride being given away by her father while the marriage service was conducted by the bridegrooms father, the Rev. Annie was born in December so there was an age dierence of 17 years between them.

The couple lived in the large red-brick semi-detached house, No. Their marriage appears to have been a successful one with three sons and a daughter resulting from the union. Reynolds habitual style of working has been lovingly recounted by his daughter, Margaret, in a letter to a relative University of Manchester Archive. Although it relates to a time in the late s for she was born only in it seems unlikely that these habits would have greatly changed with time: My father was a great worker. He breakfasted at 8 am, left for the College at by tram, worked in the laboratory until 1pm, lunched at a cafe that catered for.

I sometimes came out of town by tram and joined him. He carried his stick or umbrella at the slope over a shoulder and he never knew I was there. He was far away, and I had to make myself known to take a short cut when we were nearly home. Then he worked again all the evening, after reading the [news]papers before dinner, until 2 or 3am.

Every day alike, except Saturday afternoon and Sunday, when he went for long walks with his friends. In view of the subject of this book, the present account which draws extensively from an earlier paper by the authors: Jackson and Launder, focuses particularly on his two major papers on turbulent flows Reynolds, ; Reynolds, , although this was by no means the only subject on which he was working at that time. While our principal attention will be focused on the later analytical study, Reynolds , we first consider the experimental investigation, Reynolds , as the discoveries in that paper shaped the later publication and, moreover, had made a significant impression on one referee who was called upon to review each of the papers.

The paper Most readers will be familiar with Reynolds study of to quote from the title of his Phil. However, as noted above, some nine years before that paper appeared, he made a presentation to the Manchester Literary and Philosophical Society, On the extent and action of the heating surfaces of steam boilers which is reprinted as Paper 14 in Vol. Now, the rate of this diusion has been shown to depend on two things: The natural internal [molecular] diusion of the fluid [and] eddies caused by visible motion which mixes the fluid up and continually brings fresh particles into contact with the surface.

The first of these [mechanisms], molecular diusion, is independent of the velocity of the fluid and may be said to depend only on the nature of the fluid. The second, the eect of eddies, arises entirely from the motion of the fluid, and is proportional both to the density of the fluid and the velocity with which it flows past the surface. In a paper read to the British Association in , On the eect of oil in destroying waves on the surface of water, Reynolds associated that phenomenon with the production of turbulent eddies in the water below the surface generated as a result of the movement of the oil film under the action of the wind which caused a shear flow to be produced in the water see Paper 38 of Vol.

I of his Collected Works; Reynolds, As he related much later in a letter to his colleague, Horace Lamb University of Manchester Archive; also reproduced in Allen, on conducting an experiment on a windy day at Mr. Grundys pond in Fallowfield, he observed that by throwing a small quantity of oil onto the surface, instead of waves being formed, eddies were produced in the water beneath the oil film which took on the appearance of plate glass.

This acute observation evidently provided him with his early insight into turbulence production in wall shear flows. Returning now to the paper, the original print of the so-called Reynolds tank experiment has been reproduced in numerous articles and text books so, instead, Figure 1. The glass tube with a flared entry which is itself housed within a tank filled with water is still used to provide students with a very clear indication of the starkly contrasting states of motion, whether direct or sinuous or, in todays terminology, laminar or turbulent.

In Reynolds own words:. The internal motion of water assumes one or other of two broadly distinguishable forms either the elements of the fluid follow one another along lines of motion which lead in the most direct manner to their destination, or they eddy about in sinuous paths the most indirect possible. The existence of these two modes of fluid flow was, of course, already widely known. The first description of the transition between laminar and turbulent flow in a pipe had been provided by Hagen who used sawdust as a means of flow visualization later, he recommended the use of filings of dark amber; Hagen, Reynolds dye-streak studies and other data were, however, the first to show that, for a range of flow velocities, pipe diameters and viscosities, transition from the former mode to the latter occurred for roughly the same value of the unifying dimensionless parameter which today bears his name, the Reynolds number.

The first step in Reynolds discovery of this parameter appears to have been his observation that the tendency of water to eddy becomes much greater as the temperature rises. It occurred to him that this might be related to the fact that the viscosity of water decreased as the temperature rose. By examining the governing equations of motion he concluded that the forces involved were of two distinct types, inertial and viscous, and, further, that the ratio of these terms was related to the product of the mean velocity of the flow and the tube diameter divided by the kinematic viscosity.

In his paper he states: This is a definite relation of the exact kind for which I was in search. Of course without integration the equations only gave the relation without showing at all in what way the motion might depend upon it. It seemed, however, to be certain, if the eddies were due to one particular cause, that integration would show the birth of eddies to depend on some definite value of [that group of variables]. Reynolds earlier paper On certain dimensional properties of matter in the gaseous state one of his longest and most original had a direct impact on his discovery of the Reynolds number, as he acknowledged in his paper where he observed that: no idea of dimensional properties, as indicated by the dependence of the character of the motion on the size of the tube and the velocity of the fluid, occurred to me until after the completion of my investigation on the transpiration of gases.

In his paper Reynolds noted that kinematic viscosity is a quantity of the nature of the product of a distance and a velocity which, from his earlier work on the kinetic theory of gases, he was able to associate with molecular velocity and mean free path. This provided him with interesting alternative physical interpretations of that unifying parameter.

Of course Reynolds recognized that the critical value arrived at in his experiments with the tank sometimes called the higher critical number was not. In a second series of experiments, with dierent apparatus, he thus set about determining the value of Reynolds number below which highly turbulent motion created at entry to the pipe would decay with distance, with the flow eventually becoming laminar.

In this case, he made pressure drop measurements along a pipe for a range of velocities to delineate the mode of flow. Although in that paper Reynolds never cited the actual values, Allen concluded from the figures that he did quote that, for the two lead pipes used in this second set of experiments, the lower critical number was and while in his later paper Reynolds put the critical value between and Stokes was a pioneer in the use of the typewriter though it appears that the machine he used for his review only had available upper-case letters see Figure 1.

The first sentences gave his lofty, rather patronizing observation and verdict: This paper records some well contrived experiments on a subject which has long needed investigation the transition between the laws of flow in capillary tubes and in tubes of large diameter as employed in Engineering. I am of opinion that the results are important, and that the paper should be published in the Phil.

It then concluded: In several passages the Author refers to theoretical investigation whose nature is not suciently indicated. Rayleigh The paper was duly published and, in the years that followed, each of the referees publicly signalled the exceptional importance of Reynolds findings. More than a century after Reynolds experiments there has been considerable renewed interest in the mechanism of transition in pipe flow Eckhardt, ; Fitzgerald, with the aim, inter alia, of acquiring a more complete understanding of the development of non-linear, finite instabilities leading to transition for pipe flow is known to be stable to infinitesimal disturbances at all Reynolds numbers.

Manchester is again making important contributions to this research through the work of Mullin and colleagues Hof et al. Professor Reynolds has traced with much success the passage from one state of things to the other, and has proved the applicability under these complicated conditions of the general laws of dynamic similarity as adapted to viscous fluids by Professor Stokes.

In spite of the diculties which beset both the theoretical and experimental treatment, we may hope to attain before long to a better understanding of a subject which is certainly second to none in scientific as well as practical interest. Sir George Stokes served as President of the Royal Society from to and in this capacity, in November , he presented the Societys Royal Medal to Osborne Reynolds for his investigations in mathematical and experimental physics, and on the application of scientific theory to engineering.

More than half of Stokes citation was devoted to a summary of the paper. Although the physical significance of the dimensionless parameter we know as the Reynolds number had thus quickly become widely recognized in Britain, it was only some years after Reynolds retirement that his own name became attached to it through the publications of various German workers. Rott cites Sommerfeld as being the first to link Reynolds name with the parameter, an attribution followed shortly thereafter by Prandtl in his early paper on the Reynolds analogy, while later, in an encyclopaedia entry on fluid motion, Prandtl unequivocally announces The forementioned quantity, a dimensionless number, is named after the discoverer of this similarity, Osborne Reynolds, [and is called] the Reynolds number.

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A passing fancy Besides the immediate acclaim accorded Reynolds paper, the recent agreeable developments in his personal life his marriage to Annie, and the safe delivery of Henry Osborne, the first of their four children , not to mention his admission in as an Honorary Fellow of Queens College, Cambridge, would, one might have supposed, have had the eect of suppressing the desire, on his part, for bringing about any major upheaval in his life. When the building was nearing completion, at the beginning of , steps were taken to appoint key sta. Unwin, who following his disappointment in Manchester had, in , been appointed to a chair at Coopers Hill College, and A.

On this occasion, however, it was Unwin who proved to be the successful candidate, the reverse of what had happened in the case of the Owens College appointment. It is worthwhile pausing to reflect on the likely consequences for fluid mechanics if, instead, Reynolds had been appointed to the Chair. The building was new but unoccupied and presumably unequipped since the professors would. The first students were admitted in February from which time Unwin was appointed Dean of the Central Institution, with all the associated administrative responsibilities, on top of the task of teaching in his own department without, initially, any demonstrators or assistants Walker, Thus, it seems at least questionable whether, had Reynolds been chosen for that position, his major remaining works on fluid mechanics would ever have been written, at least in the form we know them.

The papers that would have been placed in jeopardy included not only his follow-up to the paper to which we shall shortly turn but also his very important paper on film-lubrication Reynolds, Of that Lord Rayleigh, 32 years after its publication, felt able to remark it includes most of what is now known on the subject and in celebration of which a centennial international conference was held in Dowson et al.

Reynolds disappointment at failing to secure the chair in London must have been assuaged that summer, by the conferment on him of an honorary degree by the University of Glasgow, where W.

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Rankine had formerly been a professor and where the Thomson brothers James, Rankines successor, and Sir William [later Lord Kelvin] then served. Whether this last distinction had any bearing on Reynolds subsequent action is unknown but, later in , he applied for the vacant Cavendish Professorship of Experimental Physics at Cambridge. Despite Reynolds numerous distinctions, however, the appointment went to his former student, J.

Although it has already been quoted Gibson, ; Allen, , it is worthwhile repeating part of Reynolds generous letter of congratulations sent on Boxing Day, My dear Thomson, I do not like to let the occasion pass without oering you my congratulations, which are none the less sincere that we could not both hold the chair.

Your election is in itself a matter of great pleasure and pride for me. Believe me yours sincerely Osborne Reynolds. Thus, Osborne Reynolds remained at Manchester. But what had provoked this desire to leave? Could his wife have applied pressure for them to move to a more attractive urban environment? This seems unlikely given that she had become settled in Manchester and, as a Victorian woman barely in her mid-twenties, would surely have deferred to the wishes of her husband on all things relating to his professional life.

It seems more likely that the decisions were Reynolds alone, perhaps feeling frustrated that, after 16 years in post, he. ReproFigure 1. Indeed, Thompson ; as reported by Allen, notes that in that year Reynolds drew the attention of the Universitys Council to the urgent need for an engineering laboratory. It seems that, finally, this complaint may well have led in to the overdue provision of state-of-the-art laboratories Gibson, The paper As the preceding section has indicated, in the years following publication of the paper, the unresolved questions stimulated by the work reported therein by no means fully occupied Reynolds mind.

Indeed, as the list of contents of Volume 2 of his Collected Works will confirm, he was actively exploring a number of other research interests. Perhaps for that reason, only in did he feel ready to respond to Lord Rayleighs expressions of hope for progress on the theory. On 24 May he reported orally the results of his extensive analysis to the Royal Society and thereafter submitted a written version of this work that he had had printed at his own expense to be reviewed for publication in the Phil.

By then Reynolds, whose contemporaneous photograph appears in Figure 1. He was then unquestionably the leading engineering fluid mechanicist in England and quite possibly more widely than that. Perhaps inevitably, on receiving this second manuscript on turbulent flow from Reynolds, he sent it for review by Sir George Stokes.

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This time, however, the referees response was rather unsatisfactory. After a long period of silence, on 31 October Sir George, now equipped with a typewriter with both upper- and lower-case letters, sent his reply Figure 1. The letter is a copy-book example of the on-the-one-hand. However, the reviewer couldnt confirm that view. Stokes concluding sentence seems to imply that he had finished with the matter, but Lord Rayleigh evidently had other ideas.

Although the exchanges are incomplete it seems that Rayleigh pressed Stokes to go further and, when Stokes pleaded that he had mislaid the copy of the paper, he arranged for him to be sent another copy. Since the paper had been printed, Reynolds had evidently submitted several copies. On 5 December , Sir George sent this second copy back indicating that he had now found the copy originally sent to him. He added his regrets that he was not yet able to go beyond the rough indication contained in a letter sent to Lord Rayleigh some time ago Royal Society Archive Ref.

Stokes to Mr Rix. Meanwhile, Lord Rayleigh had sent the paper to a second referee, Horace Lamb, Professor of Mathematics at Manchester, who a decade earlier had been elected a Fellow of the Royal Society. One can only speculate why Rayleigh approached the only other senior fluid mechanicist in Manchester to review his own colleagues work.

Nevertheless, on 21 November Lamb sent his longhand assessment which began with the brisk summarizing statement: I think the paper should be published in the Transactions as containing the views of its author on a subject which he has to a great extent created, although much of it is obscure and there are some fundamental points which are not clearly established. There followed three pages of detailed criticism including complaints at the inadequate definition of Reynolds term meanmean motion and a misprint in the manuscript Royal Society Archive Ref.

The Royal Society holds three further communications from the referees of which only one is dated. There is thus some doubt as to the actual sequencing though the most probable seems to be the following.

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At some point Sir George Stokes does send his review to Lord Rayleigh, a two-page typed assessment raising some of the problems with the paper he and, indeed, Lamb had aired earlier. Thereafter or, possibly, even before that communication , the referees had made contact with one another, presumably through the intervention of Lord Rayleigh, which led Lamb to prepare a joint report that Sir George attached to his letter of 30 January Royal Society Archive Ref. Dear Lord Rayleigh, I enclose what Lamb meant for a draft of remarks to be submitted to the author.

I think we are both disposed to say let the paper be printed, but first let some remarks be submitted to the author. There was very good work in the former paper, and there may be something of importance in this, but the paper is very obscure. In its present state it would hardly be understood. Yous very truly, G. The draft of remarks, in Lambs handwriting followed: Prof Reynolds Paper The referees have found great diculty in following the argument of this paper; partly in consequence of the fact that such terms as mean-mean motion and relative mean motion are used without any precise definition.

There is a well-known distinction between molecular and molar motion; but it is not clear in the case of molar motion how any physical distinction is to be drawn between what is mean and what is relative. The introduction might be greatly shortened, as a good deal of it can only be understood after reading the rest of the paper. The purport of 5 a p. The authors view does not appear to be dierent from that generally held, but it is insisted upon as something new.

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  4. The statement, in 5 b , that the ordinary equations of a viscous fluid are true only when the motion is approximately steady, is questionable. It is perhaps based on the investigation on p. It would seem as if there had been a slip in writing u for u; but at any rate there is need of explanation.

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    It is to be noted that the argument, if valid, would show that there are geometrical diculties in the way of applying the idea of mean velocity to cases other than steady homogeneous motion. The essence of the paper lies in the equations on pp. If these are clearly established a great point would be secured, but its reasoning is somewhat obscure, and needs much amplification. The conception of mean-mean-motion is a very delicate one and it is not made evident in what sense u, v, w are continuous functions, or on what conditions the derivatives, etc.

    The whole argument turns on questions of this kind, and it is just here that explanations are wanting. A margin instruction pencilled on the review in Rayleighs hand, indicated that the report was to be copied meaning that a clerk was to transcribe the review presumably for onward transmission to Osborne Reynolds. Thus, the review phase of the manuscript was brought to completion. Taking account of the four-page insert made by Reynolds in the published version, the reference here is to Equations 13 19 of the published work. I am very glad to know of these diculties and of the opportunity it aorded me of improving the paper in this particular.

    As it is by such separation of the simultaneous component of velocity at each point, introduced into the equations of viscous fluid, that the evidence of a geometrical limit to the criterion appears independently of all physical considerations, any want of clearness on this point, no doubt, confuses the whole argument.

    That I should have scamped the preliminary explanation of this part of the argument and diused it over the whole paper I can only explain as a consequence of its definite character having blinded me to the diculties which would thereby result in distinguishing what was new from what was already accepted, and of my desire to set forth the proof of the actual maintenance of the geometrical conditions under which such separation is possible aorded by experiment, as well as to indicate the general character of the mechanical-actions, expressed in the equations of motion, on which such maintenance depends.

    This head-reeling sentence, words in length, is also remarkable for its naturalness; its innocent admission of the papers weaknesses accompanied by its ready self-forgiveness. The letter then continues:. I now enclose you in M. It contains, what I hope will be found, a clear definition of the terms mean-mean motion and relative-mean motion as well as of mean-motion and heat-motions and of the geometrical distinctions between these motions.

    This passage, like those cited earlier, brings out Reynolds infatuation with long rambling sentences that stand starkly in contrast to Lambs crisply stated criticisms. He finally acknowledges: With reference to the diculties in logic of 8 p. There are, I am sorry to say, certain other misprints in the paper which must have increased the inherent diculties of the subject.

    Very truly yours, Osborne Reynolds. Apparently, no further exchanges between author and editor remain in existence and, since there is no copy of the original manuscript, it is not certain how extensive were the changes actually made. One clear indication of a change in the published version of the paper is that four pages of 5 of the Introduction are placed, entirely without explanation, within square parentheses and end with the date: Feb 18, that is, the day before Reynolds sent his response.

    Thus, this passage clearly seems to be what Reynolds referred to in his reply to Rayleigh as the full preliminary description of this part of the argument which by permission I shall be glad to substitute for the first two lines of 5. Since this was the only significant change referred to by Reynolds it appears likely that all other changes were minor, mainly consisting of corrections to typographical errors in the original. As a footnote to the above exchanges, within a few weeks of Reynolds responding to the anonymous LambStokes review, Horace Lamb was directly in touch with Reynolds seeking to check that he had correctly interpreted material in the paper when referring to it in his book Hydrodynamics which was about to be published.

    The enquiry elicited a distinctly cool response from Reynolds in a handwritten letter to Lamb dated 5 April Allen, :. Of course these dimensional facts. Nor is it polite or true to speak of the empirical formulation adopted by Engineers since it is Engineers who have done the scientific investigations which alone have given us accurate data.

    Readers may form their own opinion as to whether Reynolds acerbic response was provoked by a perception that Lamb had been one of the referees of his paper3. Despite its rather lukewarm reception by the two eminent referees, the paper is seen today as a mighty beacon in the literature of fluid mechanics. First and foremost was the decomposition of the flow into mean and fluctuating parts leading to the averaged momentum equations now known as the Reynolds equations in which the Reynolds stresses appear as unknowns.

    In fact, throughout the analysis Reynolds treated the averaging in a form akin to what is now known as mass-weighted averaging, 60 years earlier than the source that is usually quoted for introducing that strategy. It was surely just that his experiments had used water as the fluid medium that has led to this feature being ignored.

    The papers other major analytical result was the turbulent kinetic energy equation in which he observed that the terms comprising products of Reynolds stress and mean velocity gradient represented a transfer of kinetic energy from the mean flow to turbulence. As an indicator of just how far this discovery was ahead of its time, we note that the corresponding, albeit simpler, equation for the mean square temperature fluctuations was not published until the s Corrsin, Reynolds purpose in examining the turbulent kinetic energy equation was to provide an explanation of why the changeover from laminar to turbulent motion should occur at a particular value of the Reynolds number.

    Indeed, that was the driving rationale for the whole paper. For this purpose he considered fully developed laminar flow between parallel planes on which a small analytical disturbance was superimposed which permitted him to obtain expressions for the turbulence energy generation and viscous dissipation rates integrated over the channel. The relative magnitude of these two processes varied with Reynolds number and the lower critical Reynolds number he identified as being that where the overall turbulence energy generation rate had grown to balance the viscous dissipation rate.

    That his estimates were inaccurate is now seen as irrelevant since the paper contained more than enough novelty for the world of fluid mechanics to absorb over the ensuing decades. In response to Reynolds criticism, Lamb replaced empirical formula adopted by Engineers in the published book by practical formula adopted by writers on hydraulics. In he gave the Bakerian Lecture to the Royal Society Reynolds and Moorby, reporting measurements of the mechanical equivalent of heat. Of this huge experimental programme in which he obtained the equivalence within 0.

    Osborne Reynolds final years in Manchester were marked by his intense eorts to provide a mechanical theory of matter and the ether stemming from ideas contained in two earlier papers. However, in his obituary notice Lamb remarks, in what must be seen as a kind understatement, unfortunately illness had begun gravely to impair his powers of expression and the memoir as it stands is aected with omissions and discontinuities which make it unusually dicult to follow.

    Gibson has noted that was the last year in which Reynolds was able to take an active role in the department, his declining state a condition that today might have been diagnosed as Alzheimers disease leading to his retirement from the University at the age of 63 in A photograph showing part of the fine retirement portrait of Reynolds by the distinguished portraitist, John Collier, OBE, appears in Figure 1.

    In , Osborne Reynolds left Manchester with his wife and daughter to live at the vicarage in St Decumans, a hamlet on the hill above Watchet, a small though not insignificant historical port in north-west Somerset. The church and the vicarage are shown in Figure 1. Why Reynolds or, perhaps more accurately, given the prevailing circumstances, his wife should have chosen Watchet as their retirement base is unknown though the fact that both their fathers had been clergymen probably provided the essential contacts for them to have been able to rent the vicarage.

    The Census of Great Britain discloses that the return for the Reynolds household was completed by Annie on behalf of Osborne and that, numbered among the residents, in addition to their daughter, Margaret Charlotte, and two domestic sta, was a live-in sick nurse. Evidently, his final years were. Collier, OBE. There he remained until his death from influenza on 21 February His funeral in St Decumans church was attended by Horace Lamb The West Somerset Free Press, 2 March and Reynolds is buried in the churchyard, his gravestone being an elegant art nouveau cross with his name and the dates of his arrival and departure beautifully engraved thereon Figure 1.

    His wife who lived until is interred with him while two grandsons the sons of Henry Osborne Reynolds, one named Osborne Reynolds , both of whom were killed in action during the Second World War, are memorialized on the gravestone. My personal relations with him when I was a student are a very pleasant recollection; he was always very kind to me, had a winning way with him and a charming smile. He was one of the most original and independent of men. When he took up a problem, he did not begin by making a bibliography and reading the literature.

    In his lectures Reynolds was often carried away by his subject and got into diculties.