\jeff{krimmel}

A Note on G.I. Taylor

I just finished reading a book titled The Life and Legacy of G.I. Taylor[1] by George K. Batchelor. G.I. Taylor is one of the best known and most respected fluid mechanicians in that field’s history. And being a computational fluid dynamicist, I have a particular affection for the great scientists who have studied the mechanics of fluids.

But G.I. Taylor wasn’t just a fluid mechanician. He also made seminal contributions to the field of solid mechanics. He is thus more widely known as a giant in the field of mechanics in general, or in applied mathematics, depending on with whom you happen to speak. Regardless, the man was a great engineer and scientist, and the book about him written by one of his former students and a fluid mechanics giant in his own right, G.K. Batchelor, was a pure delight to read.

The first time I remember coming across the work of G.I. Taylor was as a reference[2] to a homework problem in an advanced fluid mechanics course I took here at Caltech. The paper was about how matter disperses when injected into a slow-moving fluid in a pipe. The point of the homework exercise was to derive the partial differential equations that governed the various moments of the concentration of the injected matter (taken as a passive scalar).

It was a fairly straight-forward problem, but I remember taking note of how easily readable Taylor’s paper was. It’s not everyday you stumble across papers in this field that tell you a whole story. I have learned to expect bits and pieces here and there, and then additional effort is required to bring everything together. But this was not so in this particular case, and as I later learned, most of Taylor’s papers are similarly readable.

The work of Taylor that is most relevant to my research is his study of intense explosions[3,4]. He discussed the case where a large amount of energy is deposited at a single point, and a self-similar blast wave results, propagating into the previously undisturbed fluid. The explosions I study are not so intense, but the asymptote to infinite strength explosions is nonetheless interesting. Taylor was motivated to work on this problem as a result of his involvement in the Manhattan Project.

If I could take one quote from Batchelor’s book that I thought best summarized Taylor’s method of research, it would be the following:

G.I. always took a practical view of a problem and attached relatively little value to elegant general results if they did not permit a comparison with observation.

Ironically, this quote is taken from the end of the section titled “Longitudinal dispersion in flow in tubes” in chapter 16, the section of the book in which Batchelor discusses the very paper[2] referred to in the homework assignment I mentioned. But this quote gets to the essence of who G.I. Taylor was as a researcher. He was not someone who sought out mathematical beauty at the expense of physical utility. From what I know, he always seemed to be focused on the task at hand, and he had an entirely uncanny ability to simplify the problem on which he was working and arrive at results that were applicable to a wide class of problems while still being eminently experimentally verifiable, most often by himself.

I wanted to read The Life and Legacy of G.I. Taylor for several reasons. I’ve been interested in Taylor’s work for a few years now, and G.K. Batchelor, the author of the book, is a huge name in the field as well. I’m interested in just about anything one of them had to say about the other. But I was also hoping to capture some insight, maybe some advice, that I can use regularly in my own research routine. I don’t delude myself into thinking I’ll be able to make contributions on par to Sir Geoffrey Taylor, but I will certainly use his approach as motivation to continually improve my own.

[1] Batchelor, G.K. The Life and Legacy of G.I. Taylor, Cambridge University Press, 1996.

[2] Taylor, G.I. “Dispersion of soluble matter in solvent flowing slowly through a tube.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 219, No. 1137. (Aug. 1953), pp. 186-203.

[3] Taylor, G.I. “The formation of a blast wave by a very intense explosion. I. Theoretical discussion.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 201, No. 1065. (Mar. 1950), pp. 159-174.

[4] Taylor, G.I. “The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 201, No. 1065. (Mar. 1950), pp. 175-186.