He was an expert in fluid mechanics. His understanding of a phenomenon that became known as the Saffman-Taylor instability – which occurs when a low-viscosity fluid is injected into a higher-viscosity fluid – helped the oil industry to extract trapped deposits.

His understanding of vortices led to a new mathematical analysis of the air turbulence caused by jets taking off which offered vital insight into several aircraft accidents. This work contributed to the decision to leave greater gaps being left between aircraft taking off, thereby improving safety.

Professor Saffman died in Pasadena, California, where he was the Theodore von Kármán Professor of Applied Mathematics and Aeronautics, Emeritus, at the California Institute of Technology, where he had worked for more than 40 years.

Born in Leeds in 1931, Philip Geoffrey Saffman attended Roundhay School in the north of the city. His outstanding performance led him to begin studying at Trinity College, Cambridge. There he was awarded his bachelor and masters degrees before earning his PhD. In 1958 he was appointed an assistant lecturer in applied mathematics.

He moved to the United States in 1964 after he was offered the post of professor in fluid mechanics at the the California Institute of Technology, known as Caltech. He was named von Kármán Professor in 1995.

Prof Saffman was a Fellow of the American Academy of Arts and Sciences and in 1988 was elected a Fellow to the Royal Society. He also received the Otto Laporte Award from the American Physical Society.

Prof Saffman served as associate editor for both the Journal of Fluid Mechanics and Physical Review Letters and was most recently an editorial board member for the Studies in Applied Mathematics journal .

Colleagues knew him as a soft-spoken man with a dry sense of humour as well as a leading scientist and inspiring teacher.

He is survived by his wife, Ruth; children Louise, Mark, and Emma; and eight grandchildren.