2005 Timoshenko Medal Lecture By Grigory I. Barenblatt
Applied Mechanics: an age old science perpetually in rebirth
By Grigory I. Barenblatt
Mr. Chairman, Colleagues, Ladies an Gentlemen:
I want to express my gratitude to the Executive Committee of the Applied Mechanics Division of the American Society of Mechanical Engineers for nominating me for the Timoshenko Medal, and to the Board of Governors for awarding me the Medal on behalf of ASME.
The personality and name of Stepan Prokofievich Timoshenko (Stephen P. Timoshenko as he is called in this country) is very special for me. When I was a beginning student at Moscow High Technical School, where I studied before entering the Mathematics Department at Moscow State University. I purchased his book “The theory of elasticity”: in fact, this was the first technical book in my personal library. The clarity and depth of the presentation of this difficult subject wits then and remains now for me an unsurpassed standard. Something in this book astonished me, and I addressed a question to my maternal grandfather, an eminent Professor of Differential Geometry at Moscow State University. (I was raised by his family after my mother, one of the first virologists, perished preparing a vaccine against encephalitis.) The question wits: the author is definitely a Russian (at that time in our circles nobody noticed the difference between Russians, Byelorussians, and Ukrainians). Why did his book appear in translation from English? Grandfather explained - Timoshenko emigrated after the Revolution (such people were unpopular in the Soviet Union in the late forties) - however, with a kind smile he took from his library and presented me with Timoshenko’s course on elasticity in two volumes, published in Russian in 1914 and 1916 by the Sanct Petersburg Institute of Railways Transportation, and presented to him by the author. SP got the chair at this Institute after some period of unemployment: before that he was Dean at Kiev Polytechnic Institute and was fired by the Minister of Education for substantial exceeding the number of admitted Jewish students allowed by explicitly formulated (this was important) norms. Visiting my family in Moscow last summer after learning about the award, I wanted to bring these volumes to this country, but I was warned that strict rules concerning old books would not allow it. When I already was a young scientist, I was introduced to SP during his visit to Moscow. Also, I was proud when I had seen that SP and James P. Goodier mentioned my work concerning fracture in their book.
Much later when, by the initiative of Joseph B. Keller and Milton D. Van Dyke, Dean Thomas Hughes nominated me for the Timoshenko Professorship at Stanford University I spent many happy hours working in the Timoshenko Room at the Durand Applied Mechanics Building where there is exhibited a remarkable portrait of Stepan Prokofievich. I am deeply grateful to all of them for granting me this unique experience. My collaboration with my eminent colleague and now close friend Alexandre J. Chorin started shortly before that at Berkeley and continues to this day. Alexandre visited me for working together at Stanford; therefore in one of our joint works my affiliation is Stanford University.
Mechanical Engineering and Applied Mechanics, as its part, are among the first and greatest intellectual achievements of mankind. The names of Archimedes and Galileo are known to everybody. I am sad to say that nowadays these disciplines are not popular among bright young people choosing their career. And this tendency is not a new one: it started rather long ago, apparently in the twenties. As you know, G.I. Taylor, one of the first winners of the Timoshenko Medal, worked all his life at Cavendish Physical Laboratory in Cambridge. J .J. Thompson, Lord Ernest Rutherford, Sir Lawrence Bragg, great men of science, all of them Nobel Prize winners, were the Directors of the Cavendish Laboratory during G.I.’s time. According to E.N. da C. Andrade, brilliant physicists at Cavendish who created at these times pioneering works, such as ‘smashing’ the atom, discovering X-ray radiation coming from stars, researching the structure of hemoglobine and mioglobine and, finally founding the double spiral, expressed their astonishment at how such a brilliant person as G.I. Taylor could spend his life dealing with such dull and old stuff as applied mechanics. I want to give a definitive answer. Yes, mechanical engineering and applied mechanics are old art and science. But they are also young because they are eternal art and science. It is very sad that the attitude towards mechanical engineering and applied mechanics as something of secondary interest entered the consciousness of a large and influential part of society, and this attitude cannot leave their children - future students - unaffected.
Allow me another instructive example. Years ago when I had to renew my American visa, I visited the American Consulate in Rome. Strong letters in support of my application preceded my visit to the Consulate, and I was told that the American Consul decided to process my application personally - a rare distinction. So, I was escorted to the Consul immediately and I was shocked: the Consul happened to be a rare beauty in her flourishing age: blue eyes, luxurious black hair, a truly unforgettable impression ... She understood that I was impressed, and she waited a little in asking ordinary questions, and did her job. When only a small, purely technical part of the job remained, she asked her secretary to do it, and said: ”Professor, now we have 5-10 minutes. Could you tell me what you have done in your science to deserve such letters of support?” At that time our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and myself) were working intensively on investigating the scaling laws for turbulent flows in pipes and other shear flows. We came to the conclusion that the fundamental universal logarithmic law which was in use for several decades is not quite correct, and should be abandoned and replaced by a different Reynolds- number-dependent scaling law. I have to admit that many people at that time, and some of them up to now, consider our results as controversial. However, the formulae and all available experiments definitely speak in our favor. I remind you that many similar situations have occurred in the history of science, and not only in science. For instance, when an essay of Maurice Maeterlinck, who won the Nobel Prize for his ‘Blue Bird’, was included in the Index Prohibitorum by the Catholic Church, Maeterlinck wrote “At every crossing the road that leads to the future, each progressive spirit is opposed by a thousand men appointed to guard the past.” In our case, these men can also be understood: if we are right, text-books and lecture courses should be changed and you have to bear in mind that the universal logarithmic law is taught every year in a thousand universities and polytechnic institutes. We continued to defend the truth in our seminars, lectures and publications. I had no choice: my great mentor Andrey Nikolaevich Kolmogorov, whose name is known to everybody in this audience, said: “I have lived being guided by a principle that the truth is a blessing, and our duty is to find it and to guard it.”
I return to the unforgettably charming lady Consul. I decided: obviously the elegant lady who starts and finishes her days by using the flow in pipes should be interested in such work. And I did my best to present our results in the short time given to me. The Beauty - Consul - looked at me (with her wonderful dark blue eyes!) and said: “Professor, of course, what you said is interesting, even exciting. However, frankly speaking, I am astonished. When we have someproblems with pipes, we address a plumber, not a professor with a world-wide reputation!” I was ashamed, and up to now I have a feeling of personal guilt. Indeed, now we know the structure of remote stars better than the strength of a shuttle or a dam and contrary to astronomers and astrophysicists how little we do to explain in particular to younger generations the fundamental depth and beauty of our profession and to popularize it.
Money is not yet wealth. And the leading nations of the XXI century will not necessarily be the countries having more money than others. These will be the nations where great national and global problems will be understood and appreciated by the majority of their populations. The heroes of these nations will be engineers and scientists of great vision and ability to select and explain the problems of primary importance, and to achieve the support, governmental and private, necessary to solve these problems, leading to engineering achievements that bless society.
Such engineers and scientists of great vision and organizing abilities do exist; they are among us. In due time and favorable circumstances they appear and make steps of historic importance. It is enough to remember here John Rockefeller, Thomas Aha Edison, Henry Ford, Robert Oppenheimer, Howard Hughes, and more recently W.R. Hewlett, D. Packard, and William Gates.
A remarkable example, less known, is Leo Szillard, an American physicist of Hungarian origin. It was he who recognized the practical necessity of designing the atomic bomb. He prepared the text of the letter to President Franklin D. Roosevelt, where the crucial importance of immediately starting work on the construction of the atomic bomb was emphasized in strong terms. This text was signed (not very enthusiastically) by Albert Einstein. Roosevelt decided todecline Einstein’s proposal (it is difficult to believe now, but it is possible to understand FDR: the country at that time had to carry the tremendous burden related to supplying the American Army and Allies by ordinary weapons and ammunition). When Szillard learned about the negative decision in preparation, he found a personal friend of FDR, explained to him the problem, its importance and urgency, and persuaded him to interfere. The friend visited FDR, and after dinner asked him only one question: “Frank, do you think, if in 1812 Napoleon had not turned down Fulton, the inventor of the steamer, the world map would be nowadays the same?” And FDR gave the order to start the work. The scale and value of this work - the Manhattan Project - is well known.
However, the common opinion of the layman, even scientific and engineering laymen, is that nowadays there are no such problems of the scale of the Manhattan Project whose importance for the nation and the world is understood by everybody. This is deeply wrong! Such problems do exist, and they can be understood by everybody. First of all, among these problems are large-scale natural disasters, and energy problems. I will present several examples.Tropical hurricanes. The scales of these disasters are huge, and the morale and material losses are formidable. I want to emphasize here that in fact hurricanes present a fascinating problem of applied mechanics. And, in general, Sir James Lighthill, one of the first winners of the Timoshenko Medal, considered natural disasters, in particular, hurricanes, as problems of first importance for applied mathematics and mechanics.
As far as hurricanes are concerned, the situation is as follows. As a preliminary note, I want to mention a simple calculation, by which A.N. Kolmogorov started his course on turbulence at Moscow State. He asked the listeners: What will the velocity be at the surface of the river Volga in Russia (close by its parameters to the Mississippi in this country) if by some miracle it becomes laminar ? The answer was striking: hundreds of thousands of miles per hour! Why then is it kept so slow ? The reason is that the flow is turbulent: it is stuffed with turbulent vortices, and these vortices play the role of brakes, slowing the flows. An analogy: moving along mountain slopes, drivers use chains to cover the wheels - the vortices play the role of such chains.
Sir James Lighthill proposed, on the basis of many observations, a “sandwich model” of hurricanes. According to this model in the ocean during a hurricane there exist three layers: air, sea, and “ocean spray” between them, where “the third fluid” is contained; in fact, air suspension of droplets, sometimes sufficiently large, tens of microns in diameter.
Our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and myself) considered, under some natural assumptions, turbulent flow of ocean spray. The general theory of turbulent flows carrying heavy particles, developed earlier by A.N. Kolmogorov and myself, at that time his graduate student, was used in this consideration. It happened that the droplets reduce turbulence intensity, because turbulent vortices spend a significant part of their energy for suspension of droplets. Returning to the analogy with wheel chains - the chains that are worn out become weaker. The flow accelerates under the same pressure drop. Our calculations showed that this acceleration can be very large, reaching velocities of large tropical hurricanes.
I note that the same mechanism of acceleration of turbulent flows by heavy particles was noticed earlier in the great Chinese rivers Yangtze and the Yellow River, carrying a large amount of sediment, and in dust storms, both terrestrial and Martian. And the basic question arises: is it possible to prevent, or at least reduce the strength of tropical hurricanes? Our answer is affirmative, but it requires the serious large scale work of the mechanical community. The technical problem is to suppress the formation of droplets. In principle it can be done by pouring oil on the surface of the sea. By the way, such practice is known from ancient times when on the decks of vessels several barrels of oil were reliably strengthened, and in critical circumstances the oil was poured overboard. It was noticed that the intensity of the squall was quickly reduced. There exist several attempts to explain this phenomenon, but according to our viewpoint the basic effect is the suppressing of the formation of droplets. By the way, up to now the recommendations for sailors on small boats to pour oil are routinely proposed in the literature. Of course, the oil (or some detergents which also are recommended for using under such circumstances) should be safe. There are several candidates for such materials. And I repeat - a group of enthusiasts headed by young, energetic leaders can solve this problem and do it in real time - the witches like the recent Katrina should never threaten New Orleans andother remarkable cities.
Our paper was published in PNAS a month before Katrina, and it attracted the attention of PR. I was interviewed by TV - after a preliminary make up - and when the lady, senior in the team, was asked by someone who was present, when this interview would be aired, the answer was instructive: “We have to wait for a good hurricane, then more people will pay attention.’’
The problem of forest fires, also very sensitive for the world (remember, e.g., Portugal this summer), bears some similarity to hurricanes. During a forest fire a dark layer is formed above the trees where the debris and soot are moving. They suppress turbulence in the same way as droplets in ocean spray: that is apparently the reason for strong winds and even firestorms.
Another very important matter. I think that an honest analysis, deeply based on scientific consideration of natural and technogenic disasters can be not less but very often more exciting and important than great projects like Manhattan and all these cosmology and particle acceleration enterprises. There is a difference. Money, and even Big Money, cannot prevent such analysis. But Very Big Money plus politics can do it, and in these cases a chain reaction of disasters started. An example: “Titanic”. In 1913 fundamental engineering and scientific analysis of this disaster was not performed; only much later it was understood what had happened there - the temperature was lower than the temperature of the steel embrittlement, and the vessel’s body became brittle. Twenty-seven years later: 24 May 1941 at 5:52 a.m. the HMS battle-cruiser “Hood”, the flagship of the fleet chasing the German battleship “Bismarck” made a first volley. “Bismarck” answered by a shot of a small antiaircraft gun. And at 6:00 a.m. “Hood” sank; fifteen hundred people perished, only four were saved! (The steel was supplied by the same firm as for the “Titanic” .) Thinking about this case I was astonished: 24 May, spring - it should not be cold! But read Volume I11 of Churchill’s “The Second World War” - 24 May was an extremely cold day at the place.. .clearly the temperature of embrittlement again was crossed. And again: no competent engineering and scientific analysis! Only later when the welded “Liberty” ships started to break in two halves in the North Sea (tens of thousands of people perished), such analysis was performed, and Fracture Mechanics was created. George Irwin, later a Timoshenko Medal winner, was the leader. I also participated in this work. Fracture Mechanics is now as a charming lady in her forties: a remarkable past and a lot in the future. A wonderful branch of mechanical engineering and applied mechanics! Each fracture surface can tell you a lot about both the material and the loading: those who are really interested in what happened can achieve it (of course, only if they will be allowed to obtain the fractographs!)!
I want to tell you about one more field, fully deserving the attention of mechanical engineers, and able to create a first class large scale project. Nowadays when the price of gas reliably crossed the $3/gallon line the problems of energy resources is of interest to every layman. The time when I got my Ph.D. degree was difficult for people of my ethnical origin, and after many attempts I got an offer from the Institute of Petroleum of the Academy of Sciences. I was very lucky to get this job, and since that time Petroleum Engineering is also my profession. It is very important practically - this is trivial to say. But I want to emphasize that it is remarkable as an object of applied mechanics. Many ideas which reveal themselves in such fields as gas dynamics, boundary layer theory, etc., as vague models appear in petroleum engineering as exact mathematical formulations - it is an enjoyment to deal with them. What is most important - every new oil and gas deposit presents a new scientific problem, very often leading to good mathematics. The practical problem of highest importance is to enhance oil recovery. Now the legal figure is 30 percent, so it is considered as normal if we leave in the rocks 70 percent of an irrecoverable gift of nature. But take the deposits of Southern California: Lost Hills, Bellridge. The oil there lies in diatomites: rocks of very high porosity, low strength and practically zero permeability. The exploitation of such deposits by ordinary methods, including ordinary hydraulic fracture, leads to huge losses. The oil recovery is low. To find the proper way of development of such deposits means a reliable way to reduce the energy crisis. It cannot be done without the active participation of mechanical engineering and applied mechanics - what I am saying is based on my old and recent experience. The same is true for huge gas deposits inso-called tight sands available in this country - recently I presented a lecture about this subject.
Ladies and gentlemen, colleagues, I come to my conclusion. Sir Winston Churchill, the greatest man of the last century said: “If the human race wishes to have a prolonged and indefinite period of material prosperity, they have only got to behave in a peaceful and helpful way towards one another, and science will do for them all that they wish and more than they can dream. “Nothing is final. Change is unceasing and it is likely that mankind has a lot more to learn before it comes to its journey’s end.. . .” I want to finish my speech by saying that in this future development of mankind our field, mechanical engineering and applied mechanics will play a decisive and governing role. Many fields of science and engineering will appear, become fashionable and disappear, but our branch of activity will always shine because it is eternal and perpetually renewing.