Great Souls, Complex Flows, and the Soul of a Flow

KRS: Katepalli is the village from where we moved five or six centuries ago. We have kept the name until now. There are a few Katepalli families I know, including some in the United States. But there are three or four Katepalli villages in Andhra Pradesh and Telangana, and it is not obvious which one is ours.

Anyhow, my father’s village is Thimmasandra and my mother’s is Pathapalli. Each village had less than fifty houses and a population of some two hundred. Both my grandparents were Shanbhogues [village heads] of their respective villages.

They had lands of their own, and the crops grown on them were more or less the source of income. My paternal grandfather, Nanjundaiah, was a zamindar: An inam [gift] of another nearby village was given to his great-grandfather. I don’t know why, but it permitted my grandfather to collect a sixth of the revenue from that village for his use (his brothers and cousins shared the rest). All of this was abolished after the Indian Republic was created. This was when I was growing up; things were changing rapidly those days.

Thus, I come from a completely rural background in Karnataka. For the sake of my education, particularly that of my sisters, we later moved to Kolar. I was ten or eleven years old when we moved out.

KRS: My most influential teachers in some ways were from my own family, both my grandfathers in particular. My maternal grandfather, Sitharamaiah, used to collect together a few people in his village on Saturday mornings, to clean the one and only street of the village. He wanted to maintain it well, clean it, ensure that the drainage was working and all that. That had some real impact on me.

On my father’s side, grandfather Nanjundaiah was known for his rigor in such things as money transactions and measuring crop yields. Even with his own children, he was quite precise. In fact, he never wrote a line that was not almost perfectly horizontal. That sort of thing also had a huge impact on me.

In terms of school teachers, they were really simple village folk. Most of their family members were actually farmers, while one of them somehow chose to become a teacher. They would walk to school from neighbouring villages in the hot sun, and be mostly tired by the time they got there. Once, I remember that the teacher fell asleep in the class while sitting next to the door, with his legs stretched across it. I really had to go out for a compelling reason. As I jumped out of the window, he woke up with a start. [Laughs]

The teachers may not have been very knowledgeable or professional, but they were all extremely committed. Their commitment to the cause of their students has never left me; that is their long-standing impact.

KRS: At that time, there was an adult education programme that the state was sponsoring. Grandfather Sitharamaiah had a library meant for the adults in the village. It was really a cabinet that contained an assortment of books—short stories, novels, etc. I don’t ever recall anyone from the village borrowing those books, but I started reading them.

Also, the Soviet Union and India were on very good terms then, and many books were translations from the Russian originals, like those of Maxim Gorky and Leo Tolstoy. In between might be sandwiched, for instance, the speech that Nikita Khrushchev gave in the United Nations. There was also the Tolstoy story “How much land does a man need?”, where the greedy protagonist runs around, and finally falls dead because he overran, and was too ambitious. Those sort of stories were simple and beautiful, and gave me a lot to wonder about. Triveni’s Bekkina Kannu¹ was my first novel. Only a little later I read Kuvempu’s Kanooru Heggadithi. I thought that it was the greatest novel ever written.

I was always going back and forth between the homes of my grandfathers. Grandfather Nanjundaiah had a much bigger personal library. I remember when I once asked him for a novel to read, he asked me not to waste time on reading novels, and instead gave me the Bala Kanda² of the Valmiki Ramayana. Once I finished it, after almost non-stop reading, he gave me the next Kanda, and so on.

So in those circumstances, I read a lot. Actually, that was the only thing I did outside my schoolwork, since I was really not much into sports. I was about half-way into my eighth standard when we moved to Kolar, and it was then that I encountered a public library for the first time. I went there mostly to read weeklies.

There was also a time when I had to fast during the day for one week, for medical reasons. My mother allowed me to subscribe to a private library for that week in order to keep myself occupied. That was the time I read Masti Venkatesha Iyengar, Niranjana, G.P. Rajaratnam, and all those greats. That was my serious exposure to the Kannada literature of the time.

KRS: I went to ask him to suggest a topic for an inter-hostel debate. He was upset with a member of my hostel board, and he took it out on me. The next day I went to get the topic in a sealed envelope—the topic, by the way, was “Industrialization is no Civilization”—and he was apologetic and extremely kind.

At that time, one used to collect topics for debates and essay competitions from a distinguished person, and only publicly open the sealed envelopes just 24 hours before the event. And then everybody would prepare on equal terms within the allotted time. I really loved Bengaluru. I was connected to the cultural community in the city through a few of my Bengaluru friends who knew it better. As for the engineering school itself, it was a five year course, but I could have learnt all the stuff in half that time, because it was really repetitious. I had no distractions and absorbed things fast.

There were excellent students and professors. Some students were quite sophisticated compared to me but they took me as their friend. I am eternally grateful to them. One of them was Prabha Iyengar, whom you might not have known about. She was the sole woman student in my class of sixty-odd, and she was by far the brightest of all. She stood first for the first four years, while I scored second. It was only in the last year that the situation reversed.

KRS: I can’t say that he was. My role models were actually quite different, more like Adi Shankara, Vidyaranya and Vivekananda. Great souls, all of them. I thought Shankara was particularly special, because he rescued Sanatana Dharma, so to speak, from the Buddhist influence; I still shudder at the thought that, before he died at the age of 32, he had traversed across the country on foot and established monasteries in four different corners of India.³ Vidyaranya was instrumental, at least as history is told to us, in establishing the Vijayanagara empire, which was culturally extremely important for India. By the way, he appeared once in my dreams to complain that I was wasting my time. And look at how much Vivekananda accomplished before he died, at the age of 39.

To me, those people were far more inspirational than any living person. It changed a little later on when I got into science. But until I was about 15 or 16 years old, those were my strongest inspirations.

KRS: I got interested in experiments because there is such an enormous pleasure in seeing something. That is part of the reason I took to aerodynamics and fluid dynamics, as opposed to, say, particle physics, where, broadly speaking, you see nothing directly. I think the enormous pleasure you get from working out something analytically and then having that evidence right in front of you, is very different from the one that purely theoretical knowledge could give you.

Actually, when I came to work with Prof. Roddam Narasimha, I started working on theoretical problems. I was pretty good at theory, and started working on kinetic theory of gases. Then I got into this work on relaminarization because of his nudge, and started doing experiments without him urging me to do them. When we saw an agreement between my theoretical work and the measurements that I had made, I was quite pleased.

KRS: For me, going abroad was not natural, given my rural background. I was barely knowledgeable about the world at large and Bengaluru was almost the end of my territory. So I didn’t apply to any place abroad.

But I did apply to IIT-Kanpur [Indian Institute of Technology] in addition to IISc, primarily because it had an aeronautics department. IIT-Madras also had one but it was less well known to me. I was hung up on aeronautics primarily because it was the most rational of engineering fields. People in mechanical or civil engineering could live with a factor of safety of four or five. But in aeronautics, you never could. You had to be really precise about your understanding and calculations. That is what really attracted me to aeronautics.

KRS: He was nominally on the faculty, and was rarely visible in the department. He had already become the Director. He talked to us once during the week-long orientation programme. He was extremely articulate. I remember him talking about the history of flying objects and aeronautics. He sketched a boomerang on the blackboard, which remained there for the whole week. Nobody dared touch it for the entire orientation period. [Laughs]

Many professors saw Dhawan with great awe. He was somewhat imperious with them. He had no problem giving them motivational lectures on how they should do research, and things like that. But he was very open with students. I was elected a student representative for a year, and met with him along with other students. I saw in him a very different person from his public image, occasionally exposing his own vulnerabilities.

You may not know this magazine called Blitz. In one issue of Blitz, there appeared an article complaining about IISc and Dhawan, in particular. We asked him why he chose not to respond to it, to which he responded that he could not afford to spend on it any of his institutional time as director—though it was clear that the article had pained him a lot.

I got to know him much better later on, after he retired from ISRO and the IISc directorship. He had an office in the ISRO building, and I would visit him whenever I came to Bengaluru. We talked about all kinds of things, including my own aspirations. I went to his house a few times.

KRS: Yeah, they and others came then. E.C.G. Sudarshan was the inspiration for the Centre itself, but he used to be there for only three months of the year. The intensity of activity and the liveliness at IISc changed during that period, and I was right in the middle of it.

I went a few times to G.N. Ramachandran’s lectures. He would give public lectures on math and philosophy. He was a very interesting person, but it was also clear that he was paranoid about many things. And Sudarshan by far was the most inspiring lecturer I have ever seen. I told him so some years ago and he was very pleased to hear that.

KRS: I started working on the Boltzmann equation and kinetic theory of gases and later got into turbulence.

But my interests were broader. As I said, I was taking courses in physics and math. I started a seminar series with my PhD friends. No professors were involved in it—we would read a few papers and report to the group. James Lighthill’s papers in particular were very striking, and I really learnt to write well by reading them—also later directly from Narasimha.

Then, we also had a group of people meeting ever so often, to talk about any general topic that came to our minds. We would talk informally about things like determinism vs free will, or debate political philosophies. These sessions were attended by some professors too. For a few minutes, somebody would make a case for a topic and we would discuss it for an hour or so. I also got interested in modern Kannada poetry, like the works of P. Lankesh, K.S. Nissar Ahmed, and others. There were a few of my friends who knew them personally. Despite my interest, I was only peripherally engaged with the enormous riches of Kannada literature.

It was only after the first year or two at the Institute that I had my own room in the hostel. I could study without anybody calling me a “Kudumi”⁶ or something like that. [Laughs] So I was totally involved and, for some five or six years, open to everything intellectual. I was just doing fluid dynamics along the way, one might say. There was a professor at the time, Badrinarayanan, you would probably not know.

KRS: Turbulence is usually the source of larger power consumption in pipe flows, air flights, etc. But it is also extremely useful because without it, without the mixing of various things like heat and cold, or oxygen and fuel in the case of combustion, life on Earth would not exist. Flows are designed to be turbulent inside gas turbines to facilitate mixing, but there are circumstances where they become laminar in character. That means that the flow will not be able to transport as much heat or mix substances as well as desired. This can give headaches in the design and efficient operation of these machinery. Or, a relaminarized flow an over airfoil might make it more susceptible to separation. These are examples of why relaminarization is important. At a fundamental level, how a flow that has reached turbulent status can somehow give up its proclivity to occupy huge amounts of phase space and return to a laminar-like status is both interesting and non-intuitive. In fact, many people did not believe that such a change was possible, and felt that it violated the second law of thermodynamics. But it’s not violating that law, of course, since we are dealing with open systems with external forces acting on them.

When Narasimha asked if I wanted to take a look at the problem, he was already interested in it. So we made up a little theory to explain relaminarization in one instance and published it together. I continued with this work for a few years, and even wrote a long review with Narasimha where we laid out the entire panorama of relaminarization.

Interestingly, when I went to the US a few years later, I called one of my friends who was already working there. I called his lab, but his advisor answered the phone. I mentioned my name and he said, “Oh, I know you, you are the relaminarization expert.” I was quite pleased. [Laughs]

KRS: At the time, Bob Antonia had a grant from the Australian Research Grants Commission. This grant was mostly to study the interaction between the atmosphere and the ocean. One of the first things I did was to make measurements in the sea between mainland Australia and Tasmania, called the Bass Strait. I measured various fluxes in the ocean and the atmosphere immediately above it. One of the problems was to link the measurements coming from the ocean, with those from the atmosphere.

Another project was a huge atmospheric expedition where different devices were used to measure the same physical quantity, so as to calibrate one against the other. This was a month-long expedition for which we prepared for many months in advance. It was a time when there was a near-total solar eclipse, and we measured some quantities during the solar eclipse. I learnt how to do field measurements, prepare for them, etc. I also really understood how to fix broken instruments, because you don’t have a technician to help you in the field.

By the time I went to work with Corrsin, he was around 60 years old. He had already attained a certain exalted status in the community and felt no pressure to write papers to please others. He had his own research problems on which he worked to his own tune. He had several such problems, and would suggest one of them to those he found competent.

But he was not a hands-on person. He would have this coffee hour from 10 to 11 in the morning that everyone from his lab, and some neighbouring ones would attend as well. They would talk about everything, like politics, baseball or science. That’s really the time I learnt how people I had admired and held in very high regard really thought. I felt that if only I put some effort into it, I too could think as well. That confidence was really important and transformational for me, and I was never again intimidated by big names. At that time, there was Bob Long, Owen Phillips, and other big names in oceanography and atmospheric sciences. There was also Les Kovasznay.

Clifford Truesdell is one name you might remember. Truesdell was simply unto himself. I met him several times but had only two formal meetings, the first time soon after I joined Hopkins, and he spent the whole hour complaining about G.I. Taylor and Lord Rayleigh. The second meeting happened just before I went to Yale, during which he mostly tried to convince me that there was nobody of any interest there. [Laughs] It was not true, of course!

So that was the type of department. I would write a draft of a paper and Corrsin would take some months to read it and return it with detailed comments. Aside from the coffee hour, those were really the only interactions I had with him. We rarely discussed science in front of a blackboard.

KRS: You probably don’t know this, but my fondest dream was to become a professor at IISc. Everybody in Bengaluru had told me that it would be no problem because I had a very good record: just let the authorities know about your intent, and come back whenever you wanted. So, I wrote back from Hopkins but it took about nine months to hear anything back. In the meantime, I got frustrated and thought of applying for another job.

It was then that I saw this announcement about Yale. I didn’t know much about Yale, and so went to Corrsin for his opinion. He said, “Well, it’s a reasonable place.” [Laughs] It’s actually one of the best known universities in the world. So, anyway, I wrote to Yale and got the job very quickly. By the way, it was the only place I wrote for a job. I didn’t know then how lucky I was; now I know how many places people generally apply to.

Yale was looking for somebody in my area for some ten years. They were very picky and would make an offer to somebody once in two years or so, but the person would not take it because Yale was a very tough place. I was told repeatedly during my interview that I should not expect to be tenured, but should just do some good work and go elsewhere after a few years. I was just dumb and took the job. [Laughs]

So, after I got the Yale offer, the dean of engineering at Hopkins called me to his office. He said that he had heard about the offer, and also that I was “a minor star”, and offered me a job. But I didn’t take it because I knew that if I stayed back at Hopkins, I would be under Corrsin’s shadow, which I wished to avoid. So Yale it was.

KRS: Yale’s physics department was trying to build a group in condensed matter for many years. They had tried to recruit stars like Leo Kadanoff before he moved to Chicago, and Pierre Hohenberg from Bell Labs. It didn’t work somehow, so they recruited some excellent young people.

By that time, I was either already an associate professor, or tenured as full professor. They wanted somebody who had an interest in condensed matter to be associated with physics. They asked people like Kadanoff as to whom they could entice, and he suggested my name. So that’s how the physics appointment came about.

In the math department, they started a group in applied mathematics with Raphy Coifman, Peter Jones and others. I was a very natural fit somehow, so got into the department via the applied math group.

KRS: When I went to Yale, I was not aware of much of this work, I must say. But I had a Turkish colleague, who once told me that the great thing about being at Yale was that one could go off the beaten path without worrying about what others thought: one already had a certain credibility. It was very good advice, and I took it.

At the time, Barry Saltzman, who had worked with Edward Lorenz, was a professor in geology and geophysics, and I started talking to him and got interested in nonlinear dynamics. I wrote a paper and sent copies to people like David Ruelle, James Yorke and others. That’s how my interactions began with them. I got interested in more ideas by the force of conversations with them and others. That was another expansion in my thinking. So I got interested in all kinds of nonlinear problems. My interest in mathematics and physics got expanded as well, and enabled many connections to be built.

There was a fellow, Robert Helleman, who held conferences in nonlinear dynamics two times a year. He had a strange way of doing things. He would give each speaker half an hour, or whatever. If he gauged that the talk was interesting to the audience, he would allow it to go on for twice or thrice longer than the allotted time. Otherwise, he would stand up at the end of ten minutes and say “How much more do you have?” [Laughs]

KRS: Lars died in 1976, which was before I went to Yale.

Lars retired from Yale in 1972. He was in the chemistry department, and had won the Nobel Prize. There was a strict rule at the time that you had to vacate your office after retirement. When he retired, the provost of the time, certainly not a scientist, enforced that rule on Onsager. So he went to Miami, where he did biophysics until his death four years later.

But Onsager’s legacy and legend was still there. Let me tell you a true little story. There is a graveyard next to my former building at Yale, where many important people in New Haven are buried, such as those who fought in the American War of Independence; Eli Whitney is buried there, too. Also buried are Gibbs, Onsager and John Kirkwood, with graves all near each other’s.

Kirkwood was also well known in statistical physics, and he and Onsager were colleagues in Chemistry. Though Kirkwood was not as distinguished as Onsager, he was more charismatic and was therefore the real star in the University; Mrs. Onsager, in particular resented it. Kirkwood’s graveyard has a big tombstone which says “Professor of so and so, president of American Chemical Society, winner of such and such prize, etc.” A mini CV, if you like. Next to it is Onsager’s grave which simply says “Lars Onsager, Willard Gibbs Professor, Nobel Laureate”, and continues with an asterisk. The asterisk is explained at the bottom with an “etc”, which is supposed to refer to all the achievements listed rather expansively on Kirkwood’s tombstone! This is the subtle revenge that Onsager’s family took out, on Kirkwood.

KRS: Kolmogorov was a great mathematician as everybody knows, especially probabilists. I have been told later by people like Grisha Barenblatt that he would look at the atmospheric records once in a while. A.M. Obukhov was one of his students with similar ideas. They wrote the papers side by side.

I think Kolmogorov was inspired by his own earlier work. He was thinking of the analogy of a big stone which, as one grinds it, produces smaller and smaller pebbles which are somewhat similar in shape, though different in size. He had this idea of turbulent eddies behaving the same way. Lewis Fry Richardson already had the general idea that turbulent eddies would break up into smaller and smaller ones, but did not extract an analytical structure from this physical picture. In 1941 Kolmogorov basically said that only small scales dissipate the energy which is introduced at the large scale, but there are also intermediate scales where neither the large scale properties nor viscosity is important. That gave rise to his theory. Several people derived the result independently after Kolmogorov, such as Onsager, Enrico Fermi, Werner Heisenberg and Carl Friedrich von Weizsäcker. It shows that if an idea is powerful, it will occur to a number of people, and more or less at the same time. Until 1962, however, it was not very clear whether the main result was true or not. Then H.L. Grant and others in Canada measured the turbulence in an oceanic channel, and got the five-thirds power in spectral density, consistent with Kolmogorov.

But in the same year, Kolmogorov himself said that there may be more to turbulence than his 1941 work. There is a complication known as intermittency and this subject developed in a very different direction after that. Kolmogorov is thus credited with having had two great ideas in turbulence.

Indirectly, Kolmogorov’s theory inspired people like Ken Wilson [the 1982 Physics Nobel laureate] later on, because there was no other precedent for such a scaling in other fields of physics. So occasionally, Ken Wilson would cite Kolmogorov’s work and Robert Kraichnan’s work that followed later on, as an exception to how physicists at the time used to think.

KRS: The Kolmogorov model, which is a statement on universality, would not be directly helpful if you are trying to control a flow. The general idea is that for high enough Reynolds numbers, there exists a range of scales for which Kolmogorov’s theory would apply. But in general, one has no right to expect Kolmogorov’s theory to work everywhere because in his theory the energy is introduced at the large scale and drained out by smaller and smaller scales until the smallest scale are reached, where, by viscosity, the energy is dissipated.

In practice, there are many flows where energy is not put in at the large scale but at all scales, or even only at small scales. This could make the dynamics different from Kolmogorov’s picture. To control a flow, you really need to know the behaviour of the energy-containing large scales, which are peculiar to a given flow. Kolmogorov is more about how a large number of degrees of freedom interact together to yield a collective universal behaviour of a certain type. So for flows over wings and such, the boundary layers under normal circumstances have some range of scales for which Kolmogorov’s theory might apply, but the flow is also affected by the energetic scales particular to it.

Engineers use Kolmogorov’s theory all the time, though without stating so, just as one uses the second law of thermodynamics without stating it. They use Kolmogorov’s theory, for example, to calculate the smallest scale, the resolution of computations, and things like that. However, if you want to calculate real flows, it is a different ball game altogether. That’s where models come in.

KRS: As I just said, there are scales which contain energy and those others which simply drain energy from them. There are just too many of the latter scales which cannot always be handled in practice. So for engineers, who are most often interested in the behavior of the energy-containing scales, modeling these other scales which extract energy is the crux of the problem.

To do that, of course, you have to know the details of the dynamics and how small scales extract energy from energy-containing large scales, etc. There are varieties of models to do this, some of them work very well in some circumstances and some not so well. A model may work very well on a flat plate, but when you put it on a curved plate, rotate it or transfer heat to it, things could be quite different. So, every flow has its own story.

KRS: Whether you think of it as essential physics or not, it is certainly a way in which you can calculate flows that would otherwise be impossible to calculate. What you do in LES is to model the small scales, and dynamically compute the fluctuating larger scales, by feeding in the information on small scales, perhaps derived from notions of universality. These methods are, in principle, more general than other classes of turbulence models which are interested only in mean quantities.

LES is used particularly by atmospheric physicists and others doing large-scale problems. One real problem with LES is that, when you get very close to a wall for instance, where most of the dynamics resides in the small scales, it is very difficult to know where to truncate and where to model, because essentially everything becomes dynamically important. There are many different and sophisticated ways of doing LES, but the models still possess intrinsic problems.

But what was happening was that I had been at Yale for more than 21 years. I was becoming predictable to my colleagues, and they to me. Further, Yale is not a place known for engineering, generally speaking. When you think of engineering, you think of MIT, Stanford, etc. Yale had very good people, but had very little corporate or industry reputation. My colleagues who were there for 40–50 years were unhappy about this, and complained constantly that Yale administration was not supporting them. I thought to myself—“Do I really want to become an old man, very unhappy with the place, and live amongst people whose behaviour I can predict?” I said no.

So, every flow has its own story

And the University of Maryland made an offer at the right time. I didn’t particularly ask for it. The people there were extraordinary. Michael Fisher, James Yorke, Ed Ott, Roald Sagdeev, Jan Sengers, Sergei Novikov were at this institute, whose director I became. Bill Phillips, a Physics Nobel laureate, also had a fractional appointment there, as were several others. But the institute faculty had not put their act together, and the dean who recruited me said that if I could make them work together, it would be worth it. I too thought so and went there. It actually worked.

But then, a little while later, I got this offer from the Abdus Salam International Centre for Theoretical Physics (ICTP).

KRS: I knew ICTP reasonably well because I had been there a couple of times. I knew of Abdus Salam and had even seen him from close quarters twice. Although I didn’t exactly subscribe to all his views, I knew he was a great man.

This job offer was totally unexpected since I did not apply for it. I think that Prof. C.N.R. Rao played a key role. David Gross, whom I knew from before and was chairing the search committee, called me up one day and said they wanted to offer me the job. I asked him if the job was really important at that point. He said it was. I asked: “If I turned it down, who is the next on your list?” He said, nobody. Really.

I then wrote an email to about thirty or forty people I knew, those who knew ICTP and whose opinions I respected, if I should take the job. They all told me to take it. They said that ICTP was losing its spirit, and that I was the right person to put the moral fibre back into it. I went to my wife and asked her permission. If I really wanted to do it, she said that I could do it for five years. But it went on for seven, with the last two years being somewhat stressful for us as a family.

KRS: Yes, it did. I was on the road a lot. I would go from Morocco to Thailand, and I travelled a lot and helped countries build up centres of excellence, including one in Pakistan. I tried very hard to make things better for Indian scientists. I was very busy those days, and couldn’t always concentrate on research as exclusively as I did earlier.

But I had two advantages. One is that I didn’t know much Italian, and so wouldn’t go into the city except for some formal functions. It thus created some extra time. Secondly, my family wasn’t with me so I had nothing else to do but work. I would go to work in the morning, and stay on for as long as my energy lasted, sometimes until 11 o’clock. That, too, created more time for work.

KRS: Turbulent convection is a classical problem, with nothing quantum mechanical about it. Our goal in those experiments was to work with a fluid where the Rayleigh number could be made as high as possible. The Rayleigh number has fluid viscosity and thermal conductivity in the denominator, so one way to push it up is to use a fluid that has very low values for these two quantities.

That’s why we went with gaseous helium near the critical point. Once you get there, there was no reason why curiosity wouldn’t want you to go below the \lambda-point and get to superfluidity. At that time, my colleague Russell Donnelly, was pushing me to go below the \lambda-point, and so we did. That’s how I got into quantum turbulence.

What happened was that people like Richard Feynman had postulated quantum vortices below the \lambda-point, and there was some important work by people like Joe Vinen. But nobody had actually seen them. Along with my student Greg Bewley, we devised a method to visualize quantized vortices. The experiment created some excitement that wasn’t there in the field for some time. The more measurements we made, the more we saw that there were stronger analogies with classical turbulence. But the physics of quantum turbulence is somewhat easier—you know that there are vortices, and what the vortices behave like, since their strength is controlled by quantum mechanics. We thus became even more interested in trying to see if greater insight can be had on classical turbulence by studying quantum turbulence.

KRS: Yes, integral multiples of \hbar. Therefore, you are now looking at interactions amongst vortices with fixed circulation, which simplifies our ability to calculate. Others in the field found that the energy spectral density was very similar to that in classical turbulence. For a few years, we thought that perhaps studying quantum turbulence was one way to better understand classical turbulence. And we discussed these topics in a series of workshops I had organized on the topic.

In the end, we learnt that some behaviours are similar and some are not. And so, it’s not a wholly satisfactory path to understanding classical turbulence. But quantum turbulence is very interesting in its own right, and some people have gone way beyond where I was at the time. I have to get back into it soon.

KRS: My interest in solar convection was part of the quest to understand convection in diverse circumstances. There are two main parameters in the problem—Rayleigh number and Prandtl number. If you plot various properties with these two numbers as axes, the whole “phase diagram” is more or less filled, except for the combination of very high Rayleigh number and very low Prandtl number. I have no idea how to create a laboratory flow with such attributes. But the Sun is exactly an object with a high Rayleigh number and low Prandtl number. So I felt that we had to understand what happens in this instance.

I was working off and on for some time on this problem. Then I met Shravan Hanasoge, now in TIFR, and, through him, also Laurent Gizon from the Max-Planck-Institut für Sonnensystemforschung [Max Planck Institute for Solar System Research]. They told me that if I was interested in the insides of the Sun, where we cannot measure directly, they could use seismology techniques to infer properties inside the Sun from measurements made on its surface. As you say, this is an inverse problem. That’s how I got into helioseismology; we have written a few papers together and have a joint grant, so it is moving along pretty well.

KRS: That’s the point. So I believe that new theoretical work ought to accompany this experiment that will cost more than 10 billion dollars. Same with the Ignition Facility in Lawrence Livermore [National Laboratory]. It’s a different design, different concept, but it has the same problem. Though there are some interesting ideas in fusion outside the mainstream, it is hard to know what is feasible and what is not.

On your question, I don’t really know what quantitative inspiration you’d take from the Sun to big fusion projects.

KRS: Frisch came to it from the point of view of scaling, taking his inspiration from critical phenomena. The big thing is to know that, unlike in critical phenomena dealing with equilibrium systems, the scaling exponents of non-equilibrium systems are not related to each other. That means that you have to explain the exponent of each order by using a different physical argument. First of all, a few years before Frisch’s article, there were two questions—is the anomalous scaling, as it is called, real? And how do you compute the anomalous exponents?

There is this model due to Robert Kraichnan which is very simple-minded; for that model, a group of people worked diligently to show that anomaly indeed exists and, further, that the exponents can indeed be calculated. Theoretically, it meant that there is a system for which anomalous scaling definitely exists and you knew not only how to compute it but, importantly, understood the physics behind it. Uriel might have thought that since one is able to do it for the model and one knew what the physics was, one could translate it to Navier–Stokes sooner or later; and that would be the end of the problem at least from the perspective of exponents. But this translation hasn’t happened; what was calculable for the model hasn’t yet been possible for Navier–Stokes. That’s the reason that his expectation hasn’t been met.

KRS: I gave a lecture at ICTS on this topic. What really astonished me was that Chandra declared himself to be unhappy towards the end of his scientific career. He had all the recognitions possible, and everybody thought of him as a great scientist. Perhaps he didn’t have a good work-life balance? I don’t really know whether part of Chandra’s unhappiness was because he was so single-minded in his pursuit, but it appears that way.

So I would say to youngsters that while they have to concentrate and work really hard, it does not particularly help if they do not have a kind of balance to even out the perspective. I think that would be an important lesson.

The second thing perhaps is that even though Chandra declared that he didn’t care for other people’s opinions about his work, he actually took others, like Arthur Eddington, far too seriously. That may have produced a disconnect and eventual unhappiness.

I am emphasizing the fact that many times you have to be able to say: who the heck really cares what others think? Our whole cultural and spiritual heritage tells us that the ultimate goal is not to please anyone, it is all and only about one’s own internal dynamics.

So I would say to young scientists to be serious but, aside from having a sense of balance, to be totally truthful to themselves. You should really not be worried about how you may be judged by others. You have to find a way to balance your inner being when those external decisions are not in favour. And some of them will not be.

To me, Chandra was a special person. He went to England at the young age of 19, at a time when the country was still a colony. He didn’t know anything, really, aside from some physics. What did he know about how to interact with others? And he came to the US at a time when racial prejudices were very strong. Chicago was not bad in that respect, but you couldn’t escape it if you went somewhat further south. Yet, he made it into the highest strata of scientific accomplishments.

KRS: I have mentioned a number of people but don’t know if I could name just one. Sometimes when I am feeling low, and it’s raining outside and I don’t know what to do, reading a few papers have occasionally lifted up my spirits. I would say that is great influence.

Feynman’s paper on quantum vortices [1] is of that sort; Mitchell Feigenbaum [2] wrote a beautiful paper on quadratic maps; Ed Lorenz’s path-breaking paper [3] on deterministic chaos is admirable because of its unexpectedness; Ruelle and Takens [4] wrote an extraordinary paper on turbulence without ever mentioning the Navier–Stokes equations; Leo Kadanoff’s paper on universality and scaling [5] is full of insights, as is one of Ken Wilson’s papers on the renormalization group [6]; in fluid mechanics, the unparalleled paper on boundary layers by Ludwig Prandtl [7], or closer to home, the terrific paper of Dhawan and Narasimha on transition to turbulence [8]. More broadly, the so-called EPR paper on the completeness of quantum mechanics [9]; the paper by Smoot and others [10] on the heroic measurements of the COBE radiation. Who has not admired Schrödinger’s book What is Life?[11] Or the elegance and simplicity of De Gennes’ book on soft matter [12]? Or, James Lighthill, et al’s insightful paper [13] on predictability in Newtonian Dynamics.

I take solace in the fact that science is not about cut-throat competition, putting down others to promote oneself, but is really about upliftment of the human spirit. That thought alone inspires me. When I read works I just cited, and others like them, I think: “What made the authors think that theirs was the right way to go?” They seem inspired. And hope springs eternal that I would write one like that myself.

KRS: There was a student whose relative came to see me at one time. He said that the student was thinking of quitting science, three-quarters of the way through her PhD program, but one of my papers ultimately inspired her to continue in science. There have been several similar instances. So I guess I must have written a few good papers.

But I have no exaggerated view of myself but, instead, am very hard on myself. I give myself a B+, which is not a good grade in the US.

KRS: Our spiritual heritage is that you can always improve; it’s not like you are done today. The heritage is also that the path to perfection itself is not always monotonic. The optimism is that you will someday attain that elusive perfection, though it could take a very long time, or even many births. [Laughs]

In my experience with mathematics, I was too critical of myself in not continuing with my interest in it, because proving theorems didn’t come easy to me. I moved into something else instead. Self-criticism can be stifling so it has to be used with judgment. That is why I spoke earlier on the need for a balancing force.