Professor Fritz Ursell

Professor Fritz Ursell, who has died aged 89, came to England as a refugee from Nazi Germany and became an expert on fluid mechanics and, in particular, the behaviour of waves.

His interest began after he was recruited from Cambridge University by the Admiralty in 1943 as part of Group W ( the Wave Group ), which was required to determine the rules for forecasting ocean waves and surf in advance of the landings in Normandy and the Pacific.

In the case of the Normandy beaches, forecasting waves was a relatively simple task, since the coast was protected from the Atlantic swell and distant weather patterns had little effect. Ursell, however, was assigned to a group of scientists under George Deacon that was given the more challenging task of forecasting waves for the landings in Japan, where the waves would be ocean swell generated by distant storms.

When no ideas resulted, Ursell looked at a chapter on surface waves in Lamb s Hydrodynamics and found a reference to the so-called Cauchy-Poisson problem   named after two 19th-century French scientists who had applied mathematical techniques to predict the motion of waves emanating from an instant, localised disturbance  a pebble dropped in the water, for example, or indeed a distant storm.

Ursell, who was the only member of the team who understood the complex mathematics involved, realised that by taking measurements of wave pressures on the beach and applying Cauchy-Poisson wave theory, he could calculate the time and distance of the original disturbance.

Working with Norman Barber and Jack Darbyshire, Ursell applied wave propagation theory to successive measurements of wave spectra made in Cornwall. One evening, returning to Padstow after collecting data from a wave-recorder located in Constantine Bay, Darbyshire and Ursell were apprehended by the local police, whose suspicions were aroused by the combination of a German accent (extraordinarily, Ursell was still categorised as an enemy alien) and Darbyshire s Welsh accent. In one version of the story, Ursell was released and Darbyshire detained overnight.

To determine the wave spectrum from the raw wave data, Group W developed an ingenious analogue computer, the subject of a paper in Nature in 1946, which enabled the rapid analysis of wave records and the location of storm centres which, in some cases, were as much as 10,000 miles from Cornwall.

Though they were not in time to affect the conduct of the war in the Pacific, their wave studies illuminated many aspects of wave behaviour, including refraction in shallow water and the influence of seabed friction. Most important, perhaps, was the realisation that waves in the ocean typically consist of the random superposition of waves of many different wavelengths which could best be represented in the form of an energy spectrum.

Their findings have become the basis of modern wave-forecasting, and shaped Ursell s subsequent career as a mathematical researcher in the linear theory of water waves. In fluid dynamics, he gave his name to the Ursell number, an important parameter indicating which mathematical models are appropriate for particular water waves. He also made major contributions in the field of asymptotic theory (asymptotic analysis is a key tool used in the mathematical modelling of real-world phenomena).

The son of a doctor, Fritz Joseph Ursell was born into a Jewish family in Dusseldorf on April 28 1923. He was educated in German schools, but in 1936, with the situation for German Jews becoming increasingly grim and with no prospect of a university education, he was sent to Clifton College, near Bristol.

His progress was further disrupted when, following the outbreak of war, in 1940 the British government ruled that German refugees could not live within 50 miles of the coast, and he was forced to move from Clifton to complete his schooling at Marlborough.

Ursell won a scholarship to Trinity College, Cambridge, where he graduated with a First in Mathematics Part II in 1942 and a Distinction in Part III the following year.

After his wartime work, in 1947 Ursell was awarded an ICI research fellowship at Manchester University s Department of Applied Mathematics, where he joined Sydney Goldstein and James Lighthill. He left in 1950 to take up an appointment as a lecturer at Cambridge, and in 1957 he spent a year at MIT. In 1961 he returned to Manchester as Beyer Professor of Applied Mathematics, where he remained for the next 30 years.

He was elected a Fellow of the Royal Society in 1972 and retired in 1990.

Fritz Ursell married, in 1959, Renate Zander, with whom he had two daughters.

Professor Fritz Ursell, born April 28 1923, died May 12 2012

12 July 2012 Telegraph