He was raised in Billingham, County Durham, where he attended Stockton Secondary School, and went to St Catharine's College, Cambridge in 1942.

[3][4] After graduation, with the Second World War still on-going, Stewartson began employment with the Ministry of Aircraft Production.

His research led to his first publication, "Correlated incompressible and compressible boundary layers", which was published by the Royal Society in 1949.

In 1953 he went to the United States to become a lecturer at the California Institute of Technology for a year before returning to Bristol University.

In his time there, he studied rotating fluid flows, shear layers, magnetohydrodynamics, triple-deck theory, and Reynolds number.