Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl

  • Olivier Darrigol
Oxford University Press: 2006. 376 pp. £35, $74.50 0198568436 | ISBN: 0-198-56843-6

The continuing fascination of hydrodynamics — or its modern, more inclusive offspring fluid dynamics — is due to the fact that many phenomena (such as turbulent flows) that we can observe with our unaided senses pose deep scientific problems that have not been solved to this day. Those unaided observations have led artists and scientists to wonder at the beauty, majesty and waywardness of flows over the centuries. Leonardo da Vinci's pictures of vortices, Hokusai's prints of waves, and the unknown Sanskrit poet's celebration of the splendid diversity of flowing water in current, wave, foam and spray — all these are matched by the scientist's struggle to understand flow and the engineer's attempts to manage it.

Fluid power:The Great Wave by the seventeenth-century Japanese artist Hokusai.

The governing equations of hydrodynamics were first written down by the French engineer Claude Louis Navier in 1822. Those equations (with which the name of George Stokes is also associated) remain valid, so the fact that turbulence, for example, has resisted a final solution must be attributed to the inadequacy of our mathematics to handle the strong nonlinearity of the equations and the almost universal tendency of flows to crumple into one form of instability or other except under the mildest conditions. John von Neumann saw the problem clearly when he said that “The impact of an adequate theory of turbulence on certain very important parts of pure mathematics may be even greater” (than on fluid dynamics). The basic mathematical nature of the problem is now being more widely recognized: one of the US$7 ‘Millennium Prize’ problems identified by the Clay Mathematics Institute in Cambridge, Massachusetts, has to do with Navier–Stokes solutions. Understandably, it is this very inadequacy of the mathematics that has made physical insight, clever experiments and smart approximations such prized virtues in fluid dynamical research.

Until now, anyone interested in the history of this subject has had to turn to books such as History of Hydraulics (Institute of Hydraulic Research, 1957) by Rouse Hunter and Simon Ince or to John Anderson's A History of Aero-dynamics (Cambridge University Press, 1997), both strongly oriented to specific engineering disciplines. Oliver Darrigol's Worlds of Flow is the first book to see hydrodynamics in the wider context of the history of ideas in science. The subject has finally found the distinguished historian it deserves, and the serious history it demands.

Darrigol approaches the subject through the evolution of the concepts that now describe the motion of fluids — viscosity, vorticity, waves, instability, turbulence. He begins with what he calls the small elite of eighteenth-century Swiss and French ‘geometers’ (including Daniel and Johann Bernoulli), and progresses to the engineers, mathematicians and physicists of the 19th century. During this time, the subject was divided into the ideal of the hydrodynamicist, who did beautiful mathematics that often failed reality checks, and the real world of the ‘hydraulician’ who collected useful formulas disconnected from dynamics. These two ‘worlds’ of flow evolved separately, generally with scorn for each other.

But around the end of the nineteenth century and into the twentieth, many engineers began to examine the foundations of the subject in their own rather pragmatic ways: Osborne Reynolds's studies of turbulent flow, William Rankine's analysis of shock waves and Ludwig Prandtl's many distinctive theories came to characterize an emerging ‘engineering science’. All of these were inspired by the earlier work of physicists and mathematicians, and often appealed to the Navier–Stokes equations. But they also introduced novel approximations and did not hesitate to use purely numerical methods when no analytical solutions were available. Meanwhile, the hydro-dynamicists discovered that the real-life problems that the engineers were tackling involved deep questions in physics and mathematics. The study of the instability of fluid motions — the subject of Darrigol's fifth chapter — exemplifies these developments best: the two cultures began to meet, as the formulations of William Orr, Arnold Sommerfeld and Lord Rayleigh led both to the striking work of G. I. Taylor on cylindrical Couette flow and Werner Heisenberg on flow in a channel, and to the prescient work on boundary layers by Prandtl and Walter Tollmien.

Darrigol handles these developments with scholarship, insight and charm. One of the fascinating episodes he describes is the vortex theory of matter. For William Thomson (later Lord Kelvin) the idea that matter was made up of vortex rings had an extraordinary appeal: but the theory needed vortex rings to be stable, which unfortunately they were not. It seems to me that it was such failures, amid the striking success of James Maxwell's electromagnetic theory and other exciting developments in relativity and quantum mechanics, that were largely responsible for physicists' fading interest in fluid dynamics. It was thus largely left to the applied mathematicians and the engineers to fashion whatever successes the twentieth century could claim.

Darrigol takes us through these developments in the still incomplete history of the subject with a rare balance that accurately reflects its rich complexity (although I did miss mention of V. W. Ekman's friction layer in the rotating ocean and L. F. Richardson's heroic failure at numerical weather prediction). This is a book that all practising fluid dynamicists must read: I hope there will be a paperback edition soon, so that the strange history of the subject that Darrigol describes with such insight will become part of the intellectual legacy of interested students in engineering, mathematics and physics.