Darrigol O. Worlds of flow. A history of hydrodynamics from the Bernoullis to Prandtl (794382), страница 2

Просмтор этого файла доступен только зарегистрированным пользователям. Но у нас супер быстрая регистрация: достаточно только электронной почты!

Текст из файла (страница 2)

The creation of this theory was intimately bound with the formulationof the general dynamics of connected systems, with an extension of the concept ofpressure, and with the elaboration of partial differential calculus. The importance ofthese broader innovations led nineteenth-century physicists to place great value in hydro­dynamic theory; it also led to great dismay as they recognized the absurd consequences ofthis elegant theory.As d'Alembert admitted, the paradox of vanishing resistance threatened to confme thenew hydrodynamics to the realm of pure abstraction. There was nonetheless one sort offluid motion, namely water waves, for which hydrodynamicists from Lagrange to Boussi­nesq harvested results that proved important to tide prediction, ship resistance, and shiproiling.

Chapter 2 is devoted to these important advances. Although the mathematiciansLaplace, Lagrange, Poisson, and Cauchy here obtained significant results, the more'physical', application-oriented approaches to water waves came from members of theabove-mentioned subcultures of mediation, .namely Airy, Russell, Stokes, Thomson, andRayleigh in Britain, and Saint-Venant and Boussinesq in France.

These investigatorssuccessfully explained a great variety of observed wave behaviors. In the 1870s, Boussinesqand Rayleigh even managed to explain Russell's 'great solitary wave,' which had longperplexed wave theorists.The analysis of other kinds of flow involved greater difficulties. In 1843, the foundingfather of British hydrodynamics, George Gabriel Stokes, imagined three possible waysnature could have chosen to escape d'Alembert's paradox: fluid friction, the formation ofsurfaces of finite slip of fluid over fluid, and instability leading to turbulence in the wakeviiiPREFACEof the immersed solid.

Much of the history of nineteenth-century hydrodynamics can beseen as a successive exploration of these three areas of research, to which Stokes himselflargely contributed.Chapter 3 of this book is devoted to the first option, namely, the introduction ofviscosity. Navier inaugurated this approach in 1822, by analogy with the molecular theoryof elasticity that he also invented. Although the relevant equation, now called the Navier­Stokes equation, was rediscovered four or five times, it failed to explain the hydraulicretardation for which it was intended, and only succeeded in the cases of pendulumoscillations and capillary flow.

Some fifty years elapsed before physicists commonlyagreed that this failure was only superficial and adopted the Navier-Stokes equation asthe general foundation of hydrodynamics.According to Helmholtz, viscosity alone could not be held responsible for the drasticdifference'between real flows and the ideal flows described by French mathematicians.

Forslightly viscous fluids such as air and water, the main defect of earlier theories was ratherthe assumption that the velocity of the flow derived from a potential. As is recounted inChapter 4, in 1858 Helmholtz showed that, in the lack of a velocity potential, vorticesexisted in the fluid and obeyed simple laws of conservation in the incompressible, inviscidcase. Ten years later, he argued that unstable vortex sheets, equivalent to surfaces of finiteslip of fluid over fluid, were formed at the edges of solid walls.

He thus explained thetendency of water and air to form coherent jets when projected into a quiet mass of thesame fluid, as well as the convoluted decay of these jets. This idea of discontinuous fluidmotion wonderfully bridged different worlds of flow: originally meant to solve a paradoxof organ pipes, it turned out to provide the dead-water solution of d'Alembert's paradox,an explanation of the observed velocity of trade winds, some clues about the formation ofwater waves under wind, and even an anticipation of the meteorological front theory.Helmholtz's considerations involved two special kinds of instability: the growth ofdiscontinuity surfaces at the edges of solid walls; and the growth and spiral unrolling ofany small bump on a surface of discontinuity. Chapter 5 is devoted to these and other flowinstabilities contemplated by nineteenth-century hydrodynarnicists.

Owing to the difficul­ties inherent in any mathematical investigation of these questions, opinions diverged onwhether some basic forms of perfect-liquid motion were stable or not. Stokes tended tofavor instability because he believed he could thus recover slightly-viscous fluid behaviorwithin the perfect-liquid picture. Thomson tended to favor stability because he hoped toconstruct permanent molecules out of vortex rings in a perfect liquid. Beyond this playfulcontroversy, in the 1 880s Rayleigh and Reynolds made decisive progress on the problemof the stability of parallel flow within both viscous and non-viscous fluids.By their very nature, proofs of instability provide a negative kind of information,namely, certain fluid motions that seem to result from the fundamental equations neveroccur in nature because they are utterly unstable.

Although the way a perturbation growsmay sometimes indicate features of the fmal motion, the primary source of knowledge ofthis motion was by necessity experimental. Since the beginning of the nineteenth century,both hydraulicians and hydrodynamicists were aware of the turbulent character of theflow occurring in hydraulic conduits and in open channels. As is recounted in Chapter 6,the unpredictable, confused character of turbulent flow did not scare off every nineteenth­century theorist. Saint-Venant and his disciple Boussinesq sought to describe hydraulicPREFACEixflow through large-scale averaging and effective viscosity.

Similarly, Reynolds later con­ceived a kinetic theory of turbulent momentum transport.By the end of the century, a variety of mediations between ideal and real worlds of flowhad led to the new concepts of viscous stress, vortex motion, discontinuity surface,instability, and turbulence. However, none of these conceptual innovations fully achievedthe intended mastery of real flows. Further progress resulted from the extension andorchestration of nineteenth-century concepts of flow, with a focus on rendering thehigh-Reynolds-number flows most frequently encountered in natural and technicalworlds.

A much more efficient kind of fluid mechanics thus emerged at the beginning ofthe twentieth century, based on the boundary-layer and wing theories developed byLudwig Prandtl and his disciples. These synthetic achievements, and anticipations byRankine and Froude in the context of ship design, form the subject of the seventh andfinal chapter of this book. In the conclusions in Chapter8,I examine the mechanisms oftheory evolution through application, their neglect in Kuhnian philosophy, their perva­siveness in the history of major physical theories, and the special form they take in tlw caseof fluid mechanics.By emphasizing the sort of conceptual innovations that are induced by challenges fromthe natural and technical worlds, the present history of hydrodynamics leaves aside a fewabundant developments of a more formal or mathematical nature.

4 Although this selectiveapproach conveniently reduces the amount of relevant sources, the preparation of thisbook required much original research. The historians' interest in hydrodynamics indeedseems to have been inversely proportional to its historical importance. The two mainreasons for this neglect have been the technical difficulty of the subject, and the focus ofhistorians of the nineteenth and twentieth centuries on entirely new theories such aselectrodynamics, thermodynamics, relativity, and quantum theory. There are only twoglobal surveys of the history of hydrodynamics, written by modern leaders in this field.The first, by Hunter Rouse and Simon Ince, is a useful series of short biographies ofleading hydraulicians and hydrodynamicists from antiquity to the present.

The second, byGregori Tokaty, is a historical sketch of the main conceptual advances in fluid mechanics. 5A few particular aspects of the history of hydrodynamics have received more detailedattention. To the late Clifford Truesdell we owe a penetrating account ofEuler's founda­tional contributions, which must however be balanced with Gerard Grimberg's more exactassessment of d'Alembert's role. On water waves and on open-channel flow, we haveSaint-Venant's schematic but technically competent histories, as well as recent contribu­tions by Robin Bullough, Alex Craik, and John Miles.

The profiles of polytechnique­trained engineers, who play essential parts in this story, are well described in BrunoBelhoste's and Antoine Picon's works. On .Saint-Venant's own fluid mechanics, Chiara4The best-known nineteenth-century treatises on hydrodynamics, those of Basset [1 888] and Lamb [1879,1 895], had large chapters on the Lagrangian treatment of the motion of solids immersed in a perfect liquid, thestability of vortex systems, or German mathematical theorems of potential flow, none of which receives muchattention in this book. Basset and Lamb also had chapters on the effects of fluid compressibility, including soundwaves and shock waves, which I have completely left aside.

Характеристики

Список файлов учебной работы