Philip Saffman, a professor of applied mathematics and aeronautics, was a leading expert in fluid mechanics, particularly on how liquids and gases of varying densities interact. He was best known for his study of what occurs when a fluid of low viscosity, such as water, is injected into a fluid of higher viscosity, such as glycerin.

This phenomenon, now known as the Saffman-Taylor instability, is closely related to many technologically important processes, such as flow in a porous medium, and his research was instrumental in helping oil companies to develop the best methods of recovering trapped oil by injecting water or steam to force the oil to the surface. A world expert in the field of turbulence, Saffman also made fundamental contributions to the understanding of vorticity, the way, ships move through water and aircraft through air.

His precise mathematical analysis of the turbulence in the wake of jet aircraft during takeoff allowed him to calculate how long it takes turbulence to dissipate, for example after jet aircraft take off. This determines when another aircraft can safely follow.

He helped to explain the conditions that contributed to several aircraft accidents, including the crash at Dallas in 1985 of a Delta Air Lines flight which tried to land in a thunderstorm. Saffman’s work helped to persuade air-traffic controllers to allow a minimum period between take-offs to let the turbulence in the wake of the preceding aircraft subside.

Philip Geoffrey Saffman was born in 1931 in Leeds. He was educated at Roundhay School, Leeds. In 1956 he went to Trinity College, Cambridge, where he received his bachelor, master and doctorate degrees. In 1958 he was appointed an assistant lecturer in applied mathematics at Cambridge.

In 1964, after teaching applied mathematics at Cambridge and King’s College London, he moved to the US as professor of fluid mechanics in the Division of Engineering and Applied Science at the California Institute of Technology (Caltech). In 1995 he was named the Theodore von Kármán Professor of Applied Mathematics and Aeronautics at Caltech.

In 1988 he was elected a Fellow of the Royal Society. He was a Fellow of the American Academy of Arts and Sciences and was awarded the Otto Laporte Award by the American Physical Society. In addition to his numerous papers in scientific journals he was the author of Vortex Dynamics (1992).

Saffman was known to colleagues and friends as a soft-spoken man with a dry sense of humour, who only commented about things when he really understood them.

He had a rare ability to explain complex results in simple ways. He was a first-rate scientist, committed to the highest standards of scientific excellence, and an inspiring teacher. He was an enthusiastic camper and hiker.

His wife, two daughters and a son survive him.

Professor Philip Saffman, FRS, expert on applied mathematics and aeronautics, was born on March 19, 1931. He died after a long illness on August 17, 2008, aged 77