The cause of death was heart failure, said a colleague, Dr. Grigory Isaakovich Barenblatt, professor of mathematics at the University of California in Berkeley.
Mr. Lighthill was trying to repeat a swim he first made 25 years earlier, for which he applied a scientific approach using a ''two-arm, two-leg backstroke, thrusting with arms and legs alternately.'' His body was found in rough seas off Sark.
Mr. Lighthill, who was the Provost of University College, London, from 1979 to 1989 and who held the Lucasian Chair of Applied Mathematics at Cambridge University in the 1970's, a position in which he preceded Stephen Hawking, made early discoveries in mathematical modeling of how creatures swim, fly and move about.
He published his first scholarly paper when he was 19 years old and just a year out of Cambridge University. It concerned supersonic airfoil theory, and led to his innovative work in aerodynamics, which influenced the development of jet aircraft. His work on a dart-shaped supersonic aircraft was central to development of the Concorde.
In the 1940's he carried out research in aerodynamics at the National Physical Laboratory in Teddington, England.
In 1997, the Oxford University Press published his collected papers, four volumes embracing topics like reducing noise from jet planes and nonlinear fluid mechanical accoustics, a science he founded with a single scholarly paper written at age 32.
He held the Beyer Chair of Applied Mathematics at the University of Manchester and was director of the Royal Aircraft Establishment at Farnborough from 1959 to 1964. He was knighted in 1971.
Mr. Lighthill is survived by his wife, the former Nancy Dumaresq, their four daughters and a son.
By FORD BURKHART, August 2, 1998 © The New York Times Company