Whether we are designing aircraft, modelling blood flow, studying propulsion, lubrication or the dynamics of swimming, constructing wind turbines or forecasting the weather, we need to use the Navier-Stokes equations. These equations are capable of describing fluid flows over a vast range of scales. Scientists use them in fundamental studies of turbulence, and the properties of their solutions are among the great unsolved problems of mathematics.
George Gabriel Stokes was born in Skreen, Co Sligo, on August 13th, 1819, the youngest of seven children of Rev Gabriel Stokes, a rector of the Church of Ireland. From an early age, he showed clear signs of brilliance, his schoolteacher recording that “Master George was working out new ways of doing sums, far better than those given in the book”.
After education in Skreen, Dublin and Bristol, Stokes matriculated to Pembroke College in Cambridge, graduating in 1841 as senior wrangler, gaining first place in the entire University of Cambridge in the Mathematical Tripos, the final mathematics examinations. Success in the Tripos was a passport to the career of one’s choice. As a relative wrote to Stokes, he had but to decide whether he would be “prime minister, lord chancellor or archbishop of Canterbury”.
Following his success in the Tripos and his winning of the Smith’s Prize, Stokes was made a fellow of Pembroke College. Just eight years later he was appointed Lucasian professor of mathematics, a position he held for more than 50 years. This prestigious chair had earlier been held by Isaac Newton and more recently by Stephen Hawking.
Stokes’s collected mathematical and physical works, published in five volumes, contain about 140 papers. Stokes was also an active correspondent via the penny post: more than 650 letters survive from Stokes to another giant of Victorian science, Belfast-born William Thomson, later Lord Kelvin. Stokes’s scientific interests were very broad, and his correspondence covers a wide range.
In 1859 Stokes married Mary Susannah, daughter of Thomas Romney Robinson, an astronomer at Armagh Observatory. George and Mary had five children. Stokes won many honours during his life, and his name is preserved in many scientific contexts, including Stokes’ Law (fluid dynamics), Stokes’ Theorem (vector calculus), Stokes drift (oceanography), Stokes shift (fluorescence), the Stokes phenomenon (asymptotics) and several more.
Physics of fluids
Stokes made profound contributions to hydrodynamics, his most important being the rigorous establishment of the mathematical equations for fluid motions, and the theoretical explanation of a wide range of phenomena relating to wave motions in water. The Navier-Stokes equations are the universal mathematical basis for fluid dynamics problems.
Claude-Louis Navier’s original derivation in 1822 of equations for viscous fluid flow, was not widely accepted. Stokes provided a rigorous derivation founded on more secure and realistic assumptions. He investigated the internal friction of fluids, explaining how small droplets are suspended in the air and giving an answer to the age-old question asked by children: why don’t clouds fall down?
Stokes’s work combined mathematical sophistication with a great experimental facility. He devised and performed many ingenious experiments in optical science and gave brilliant theoretical explanations of the results. His work in optical science gave evidence in support of the wave-like nature of light. He carried out a spectral analysis of blood, discovering out how the oxygen is transported by haemoglobin. He helped the renowned instrument-maker Howard Grubb to construct achromatic lenses for telescopes, and he visited Birr to advise the earl of Rosse on the construction of his telescope.
A particular focus of Stokes’s work was wave phenomena in various media. He made some major advances in the mathematical theory of diffraction, polarisation and stellar aberration. Stokes elucidated the strange phenomenon of fluorescence with a radically new theory. Objects are normally invisible in ultraviolet light, but a fluorescent body emits light at a lower frequency (or different colour) than the incoming light.
Stokes was aware that fluorescence can be found in many biological systems, particularly in the marine environment. He realised that his work on fluorescence offered a way to detect ultraviolet light, to measure the UV spectrum of sunlight and other sources and to assist in chemical analysis and spectroscopy. We benefit from his work through fluorescent lamps; these use electricity to excite mercury atoms, which then cause a phosphor coating to fluoresce, producing visible light.
Climate change and its consequences are among the most pressing problems facing humanity today. There are enormous uncertainties concerning the future climate, and the best means we have for reducing these is by means of predictions based on computer simulations. At the heart of every climate model lie the Navier-Stokes equations. The same models are used regularly for short and medium range weather forecasts. Over recent decades there has been a dramatic improvement in the accuracy and scope of computer forecasts, with enormous benefits for human society. Thus the fundamental work of Stokes underlies one of the greatest scientific advances of the 20th century.
Stokes, growing up on Ireland’s Wild Atlantic Way, was a skilled swimmer and a keen observer of nature. During holidays in Ireland, he undertook observational studies of waves and swell. He examined the question of the highest possible periodic wave, and showed that the wave of maximum height had a crest with an angle of 120 degrees, in agreement with his observations.
Stokes explained the phenomenon of group velocity, where energy can travel faster than individual waves. Group velocity is of immense importance in weather forecasting. The group velocity of atmospheric waves is greater than the phase speed. Through its action, a new storm can appear “spontaneously” downstream of an existing chain of storms; the propagation of energy is more rapid than the movement of the individual storms.
President of the Royal Society
In 1851, Stokes was elected a fellow of the Royal Society along with William Thomson. He would have interacted with another Irish-born scientist, John Tyndall and with Thomas H Huxley, both of whom were strong evolutionists. Although Stokes was firmly in the “creationist” camp, he remained on friendly terms with Darwin.
With four church men in his immediate family, George Gabriel remained pious all his life, with a stern religious outlook influenced by a staunch Anglican ethos. Stokes was of a taciturn demeanour and never engaged in small talk. The single recorded exception was an animated and humorous conversation with a young American lady who, hearing that he was a mathematician, asked him “Do you prefer algebra or geometry?”
In 1854, Stokes became secretary of the Royal Society and he was president from 1885 to 1890. He was a gifted administrator and, in these positions, he was able to provide assistance and support to a large number of younger scientists.
Although his entire professional career was in Cambridge, Stokes never forgot his origins in Skreen, and returned to Sligo and elsewhere in Ireland regularly for summer vacations. In one of his heavily mathematical papers he wrote of the surf that “breaks upon the western coasts as a result of storms out in the Atlantic”, recalling the majestic rollers thundering in as he strolled as a boy along Dunmoran Strand near Skreen.
A collection of essays, George Gabriel Stokes: Life, Science and Faith, has been published recently by Oxford University Press