An eminent fluid dynamicist reminisces about her mentor’s many distinguishing qualities
On a bus journey long ago, I fell into a chance conversation with the enthusiastic high school student sitting next to me. She confided her dreams in me: she dearly wished to be a pilot. If this didn’t happen, she had a priority list she would go down until something worked out: become an academic researcher in aeronautical engineering, work as cabin crew, air-traffic controller, aeroplane mechanic, airport ground staff, and travel agency employee. This was the craziest future plan I’d ever heard, so I told Roddam Narasimha about it. RN’s face lit up in the most excited way and he literally screamed, “Where is she? Bring her to see me. Such people are precious!” He was disappointed that I had not got her contact details. When he was very young, he had been similarly enthralled with aircraft and anything to do with them.
RN made immense contributions to science and to various national missions, and was a builder of institutions. Much has been written about these, so this tribute focuses instead on the unique person he was. He has left a big void in the science world and huge voids in the hearts of large numbers of students, colleagues and friends. He leaves behind his wife, Dr Neelima Narasimha, a doctor, and his daughter, Prof Maithreyi Narasimha of the Tata Institute of Fundamental Research (TIFR).
How the boundary layer in a flow past a solid body (like an aircraft wing) transitions from laminar to turbulent is a crucial question that is not fully resolved. The picture here tells the story of a single-author paper RN wrote at the age of 24 (On the Distribution of Intermittency in the Transition Region of a Boundary Layer, Journal of the Aeronautical Sciences, 24, 711-712, 1957), which completely changed the way this process was understood. This is a top view of a flat plate over which wind blows at a speed U, creating a growing boundary layer. The words at the bottom are in his own hand.
Until then it was believed that downstream of a particular location, which he here calls xt, turbulent spots were born randomly in space, growing bigger in a self-similar manner by destabilising the neighbourhood as they got convected, until asymptotically taking the boundary layer to fully developed turbulence far downstream. RN realised that this was not consistent with experimental findings. He proposed a ‘concentrated breakdown’ near xt. Upon incorporating this into the model, the ensuing intermittency (fraction of time for which the flow is turbulent) was a universal function of the streamwise coordinate x when suitably scaled. It agreed very well with a host of experiments. A concentrated breakdown is also on sounder theoretical footing than random breakdown.
The fluid dynamics of clouds was in its infancy when RN started working on it. If a rising cloud, effectively a wet plume, behaved like other plumes, it would dilute itself into annihilation. RN showed, by using an ingenious cloud-in-the-lab, simulations and scaling arguments, that heating due to condensation along its way is key to reducing entrainment, and indeed to the existence of a cloud. RN and his student KR Sreenivasan in the seventies showed that turbulent flow can relaminarise, and that acceleration in the flow provided a mechanism. These are just a few examples showing that he set trends rather than followed them.
[H]e set trends rather than followed them
I had the privilege of being RN’s PhD student in the Department of Aerospace Engineering at the Indian Institute of Science as an external student. I was working then at the National Aerospace Laboratories where RN was Director. Later, I was his colleague in the Fluid Dynamics Unit, which he founded, in the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR). To me and to all his students, RN was a mentor par excellence. His style was to encourage us to define our own problems and research areas, which meant that he mentored students on a range of topics: nonlinear dynamics, mathematical aspects of fluid dynamics, aerospace, atmospheric sciences and the Indian monsoon. He would nudge us to turn our question into something bigger and better, and force us to think about the big picture, and about the connections of our work to questions in other areas. And then allow us to sort it out. He thus raised our standards hugely, while appearing to only mentor from the sidelines.
He was so busy in those days that I met him for an average of five minutes a few times a year, but was blown away by his insight every time. On boundary layer stability, I was trying to obtain first order corrections to the answer in a small parameter called epsilon. He saw that the effects I was getting were much bigger than O (epsilon), and opined that I had a singular perturbation problem on my hands. Armed with this knowledge, I could derive the correct lowest-order equations for boundary-layer stability, and develop code to predict transition to turbulence over aircraft wings in a few seconds on a PC which were hitherto done on a large mainframe over days. Boeing Aerospace acquired our code and found it useful.
In the 1980s and 1990s, RN taught a famous fluid mechanics course for several hours every Sunday in IISc, which had no textbook, no stipulated syllabus, no credits and no exams. A crowd would attend, and would benefit from his unique perspective and mastery over fluid mechanics. He fielded every question with utmost patience.
I would like to best remember him from the tea-table conversations at JNCASR. His original thoughts and detailed investigations, whether on Saki’s writings, on Tipu Sultan’s rockets, on the dynamics of societies which perceive themselves at risk and a whole host of other topics, were discussed over snacks and several cups of tea, and are testimonies of his brilliant mind, his penchant for reading, and his deep understanding of areas outside fluid mechanics.
One of RN’s colleagues termed him a “gentle giant” and I hope the reader has understood why.
Rama Govindarajan is a faculty member at the International Centre for Theoretical Physics (ICTS), Bengaluru.
This article was originally written for an ICTS News Special Issue in memory of Roddam Narasimha.
