Recollections of Chandra

Subrahmanyan Chandrasekhar is the subject of a splendid remembrance in the December 2010 issue of PHYSICS TODAY. From 1956 to 1966, I was in the physics department at the University of Chicago, and Chandra was my colleague and best friend. I would like to add some recollections of his work on hydrodynamics, which has unfortunately been neglected in almost all celebrations of his life.

I was a graduate student at Yale University from 1952 to 1956, working with Cecil Lane and Lars Onsager on the superfluidity of helium-4. Those of us studying quantum fluids found we had to learn a lot about classical fluid mechanics, because most probes of superfluids are hydrodynamical in nature. Onsager introduced me to the subject of hydrodynamic stability and mentioned the names of the leading investigators, whom he called a “rare crew”: C. C. Lin at MIT, G. I. Taylor at Cambridge University, and Chandra. Onsager introduced me to them all at an American Physical Society (APS) meeting in New York City. Once Chandra got to Chicago, he and I tried to calculate the hydrodynamic stability of superfluid helium between rotating cylinders¹—the Taylor–Couette flow—but our paper was based on still incomplete equations of motion for the two-fluid theory. It took another 34 years to finally get theory and experiment complete.² 

Intellectually, Onsager and Chandra were very different men. Onsager had unmatched insight into the nature of many fields but found it difficult to convey his insights to others. Chandra had less physical insight into experiments, but once he had “done the math” he could explain it to anyone on the street.

Chandra’s work in fluid dynamics is essentially forgotten in mainstream physics. I think that is because astrophysics, especially general relativity, is much more popular in the physics community than fluid dynamics; I am not aware of an undergraduate course in fluid dynamics being taught in any physics department. Also, Chandra had the bad luck of turning to fluid dynamics just before computers became generally available, and his numerical methods are not used today. His calculations were done on a Marchant mechanical calculator by his incredibly hard-working assistant, Donna Elbert. We used to call her “Miss Canna Helpit.”

When I arrived at Chicago, Chandra had obtained substantial grant support to have stability experiments done in collaboration with Dave Fultz, a geophysical fluid dynamics expert. The grant included funds to convert an old cyclotron into a hydromagnetic stability facility that used mercury as a test fluid (see photo, above).

Chandra was passionate about the experiments and was often in the lab urging us on. He brought to the lab all his visiting friends, including his mentor, Paul Dirac. Chandra was intimately involved in each experiment. In the planning stages he, our instrument maker Jim Radostitz, and I would meet in Chandra’s office and discuss the design. Sometimes we would have a race to see whether calculations or experiments would be the first to provide data on a new problem. Although Chandra’s focus was on the onset of instability—the linear stability problem—our data provided insight into nonlinear stability, such as the torque beyond the onset of instability in Taylor–Couette flow as studied with a rotating cylinder viscometer.

Eventually Chandra gathered all his calculations and experiments and put together a book entitled Hydrodynamic and Hydromagnetic Stability,³ by far the most cited of all his books. The day the first copy was received in 1961, Dave Fultz put Chandra in front of our Taylor–Couette apparatus and got the picture shown on page 10.

Chandra’s theoretical and experimental work in fluid dynamics was very productive and influential. Chandra was an early supporter, with John von Neumann and others, of forming APS’s division of fluid dynamics, and he served as division chairman in 1955. Today the division is one of the most rapidly growing in APS.