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Air flowing over an aircraft wing starts smooth and orderly, then somewhere along the wing it turns into churning turbulence. That change matters for drag, heating and fuel. Most textbooks show it as a sharp line. Roddam Narasimha spent much of his career showing it is not a line but a zone, and that flow can also go the other way. This post covers his life, his two big ideas, a worked example and what students can learn from how he worked.
Who was Roddam Narasimha?
An obituary in Physics Today by K. R. Sreenivasan says Narasimha was born on 20 July 1933 in Bangalore, where his father taught physics at Central College. He studied mechanical engineering at the Government Engineering College in Bangalore, graduating in 1953. A Spitfire aircraft he saw in a quadrangle at the Indian Institute of Science (IISc) drew him to a master's in aeronautical engineering there, under Satish Dhawan. He did his PhD at Caltech from 1957 with Hans Liepmann, and returned to IISc as an assistant professor in 1962. He died in Bangalore on 14 December 2020.
The Royal Society's biographical memoir, also by Sreenivasan, lists his research: turbulent flows, including the transition from laminar to turbulent flow "and vice versa", the kinetic theory of gases and the structure of shock waves, nonlinear dynamics, and tropical meteorology motivated by the monsoon.
What did Dhawan and Narasimha find about transition?
Their 1958 paper in the Journal of Fluid Mechanics, Some properties of boundary layer flow during the transition from laminar to turbulent motion, looked at the boundary layer on a flat plate. Its abstract describes transition as the intermittent production of turbulent spots. Assuming the spots start at random in a narrow region, they extended an earlier probability calculation and could explain why transition regions on different plates look statistically alike.
The key quantity is the intermittency factor: the fraction of time the flow at a point is turbulent. It is 0 in smooth flow and 1 in fully turbulent flow. The abstract reports that mean velocity profiles in the transition zone form a one-parameter family, with intermittency as the parameter, and describes a simple way to measure intermittency with a Pitot tube. Sreenivasan writes that this first work "catapulted him to fame" and is still cited. Narasimha later reviewed the subject in The laminar-turbulent transition zone in the boundary layer (1985).
Can turbulent flow become smooth again?
Yes. Physics Today calls relaminarization, the set of ways an initially turbulent flow can become laminar, "one of his abiding interests". With Sreenivasan he wrote the review Relaminarization of Fluid Flows (1979).
What else did he build?
The obituary records that part of his research group became, in 1982, what is now the Centre for Atmospheric and Oceanic Sciences at IISc. He conceived the Monsoon Trough Boundary Layer Experiment in the Indo-Gangetic Plain in 1990 and the Indo-French satellite Megha-Tropiques, launched in 2011 to study tropical clouds. He was director of the National Aerospace Laboratories for 10 years, then director of the National Institute of Advanced Studies, and set up an engineering mechanics unit at the Jawaharlal Nehru Centre for Advanced Scientific Research. He was also the longest-serving member of the Indian Space Commission.
Worked example: where does transition start?
The Reynolds number for flow along a plate is Re = Ux/ν, where U is the flow speed, x is the distance from the front edge and ν is the kinematic viscosity. The numbers below are sample values for a classroom example.
Take air with ν = 1.5 × 10⁻⁵ m²/s flowing at U = 20 m/s, and suppose transition begins at Re = 5 × 10⁵, a common textbook figure for a smooth plate.
Rearrange: x = Re × ν / U.
x = (5 × 10⁵ × 1.5 × 10⁻⁵) / 20 = 7.5 / 20 = 0.375 m.
So the first turbulent spots appear about 38 cm from the front edge. Now the intermittency idea: suppose a probe a little further back records turbulent flow for 30 ms out of every 100 ms. Its intermittency factor is 30/100 = 0.3. Further downstream the value climbs towards 1.
Common mistakes: using dynamic viscosity (in Pa s) where kinematic viscosity (in m²/s) is needed, and treating the transition Reynolds number as a fixed law of nature. It depends on how smooth the plate and the incoming flow are, which is why Dhawan and Narasimha linked it to the rate at which spots are produced. For the Reynolds number in pipes, read about Osborne Reynolds and the dye streak.
What can a student take from how Narasimha worked?
Look closely at the boundary. The textbook line between smooth and turbulent hid a whole zone of physics.
Use probability for messy things. Random spots, described statistically, made the transition zone predictable.
Ask whether a process can run backwards. Relaminarization came from asking exactly that.
Flow patterns are easier to understand when you can change the speed and watch them. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. For his teacher's story, read about Satish Dhawan.
Next step: redo the worked example for water, with ν = 1.0 × 10⁻⁶ m²/s and U = 2 m/s.
