[11] Narasimha started his research career at Caltech, working on the problem of jet engine noise reduction.

After the launch of the Russian Sputnik and the resulting interest in space programs, he shifted focus to rarefied gas and fluid dynamics, working with Hans W.

[12] He continued this research at the NASA Jet Propulsion Laboratory, where he went on to study aerodynamics and supersonic flows toward better understanding of the structure of shockwaves.

[12] He returned to India in 1962, and joined the Indian Institute of Science as a professor in its aeronautical engineering department (1962–1999), where he continued his fluid dynamics research, studying turbulent flow and relaminarisation, including the study of fluid flow from turbulent (chaotic) to laminar (streamlined) forms.

[12][13] He was the ISRO K. R. Ramanathan distinguished professor at the Indian Institute of Science (1994–1999), Director of the National Aerospace Laboratories (1984–1993), Director of the National Institute of Advanced Studies (1997–2004) and the Chairman of the Engineering Mechanics Unit at Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore (2000–2014).

[12] During his time at the National Aerospace Laboratories, Narasimha led the research initiative into parallel computing as a means to solve fluid dynamics problems.

At the Indian Institute of Science, his research included the ‘bursting’ phenomenon in a turbulent boundary layer,[18] non-linear vibration of an elastic string,[19] equilibrium and relaxation in turbulent wakes,[20] relaminarization,[21] hydrodynamic instability,[22] wall jets[23] and the study of clouds[24][25] as volumetrically heated jets.

[27] He also studied gas turbine blades,[28] turbulent free shear layers[29] and proposed a novel wing design for turboprop aircraft.