Plus Change

Prandtl’s boundary-layer theory provided the material that might give sub­stance and depth to the “scheme” of the wing theory. It suggested that inviscid approximations might be replaced by a more realistic account of the physics of viscous processes. The boundary layer became the focus of a sustained British research effort organized by the Fluid Motion Panel of the Aeronauti­cal Research Committee. The original intention was that Lamb would be the editor of the volumes that would draw the results together, although Fage, who clearly found Lamb’s work very demanding, put in a request that the mathematics should be kept as simple as possible. “Lamb’s Hydrodynamics,” said Fage in the course of a discussion of the proposed monograph, “was more suitable for the professional mathematician and was very difficult.”88 In the event, Lamb did not live to complete this task and it fell to Sidney Gold­stein. Goldstein had been a pupil of Jeffreys’ but he had also gone to Gottin­gen after the war to study with Prandtl.89 Despite continuing resistance, it is clear that the overall strategy that Prandtl had adopted in his Wright Lecture had been an appropriate one. He had engaged with the preoccupations of the British experts with viscous and eddying flow while reminding them of the intellectual resources that Gottingen had to offer.90 Writing to Prandtl, after the Wright Lecture, Major Low said that he had spoken to many mathemati­cians and physicists and they all said that “your paper will give a new direc­tion to aerodynamic research in this country.” Low identified the transition from laminar to turbulent flow as the special point of interest for the British audience.91

This concern with the boundary layer and turbulence became the new research front, and it was congenial territory for the British even though their head-on assault on the Navier-Stokes equations had proven frustrating. If the battle for circulation in the theory of lift was over, the war on turbulence in the boundary layer was about to begin.92 But even here the old worries were not far beneath the surface. On February 6, 1930, members of the Royal Aeronautical Society discussed a report titled “Modern Aerodynamical Re­search in Germany.”93 The report was presented by J. W. Maccoll, who had visited Gottingen and Aachen.94 Maccoll, who had a command of German, was a government scientist and was to hold the post of research officer in the Department of External Ballistics at the Woolwich Arsenal. He described in mathematical detail the original work on the laminar boundary layer and then the more recent work on the transition to turbulence. In the discussion that followed Maccoll’s paper, Bairstow identified what he saw as two fun­damentally different approaches to the current problems in fluid dynamics.

Bairstow declared that he had “been impressed by the extreme complication of the whole subject and the apparently little connection between the Ger­man methods of solution and the equations of motion of a viscous fluid. All would have noticed how often new variables were introduced into the equations to deal with failures of the original hypothesis. It seemed that the Germans were making an engineering attempt to get solutions of practical value and had little hope of solving the equations of motion in a sense that would satisfy Professor Lamb” (697).

Bairstow was describing, albeit in a one-sided way, the difference in ap­proach between a mathematically sophisticated engineer, adopting the meth­ods of technische Mechanik, and that of a mathematical physicist drawing on the finely honed traditions and research strategy of the Cambridge school. Bairstow might not have sat the Tripos, but he still took Prof. Lamb as his reference point.95 The difference in approach to which Bairstow was alluding, between the Cambridge and Gottingen traditions, has been present in one form or another throughout the story I have been telling. It was implicated in the original British dismissal of the circulatory theory, and it was central to the manner in which the theory was finally accepted by the British.96

In an article titled “Twenty-One Years’ Progress in Aerodynamic Science” which Bairstow published in 1930, the same year as the remarks just quoted, he surveyed the work that had been done since the creation of the Advisory Committee for Aeronautics in 1909. Bairstow invoked a revealing compar­ison to describe the discomfort that still surrounded the relation between the theory of viscous and inviscid fluids in aerodynamics. He likened the problem of reconciling the viscous and inviscid approaches to the problems that British physicists were experiencing in reconciling the wave and particle conceptions of light and of the electron. Two fundamentally different models were in use, but it was impossible to see how they could both be true.97 Bair­stow quoted the exasperated response to this situation of one of the country’s leading physicists, a response that mirrored, perhaps, the frustrations of Bair – stow’s own work on the Navier-Stokes equations. “Aerodynamic theory,” said Bairstow,

is now rather like the physical theory of light; Sir William Bragg recently said that physicists use the electron theory on Mondays, Wednesdays and Fridays, and the wave theory on alternate days. Both have uses but reconciliation of the two ideas has not yet been achieved. So it is in aeronautics. In our experi­mental work we assume that viscosity is an essential property of air and the building of a compressed-air tunnel is the latest expression of that belief. The practically useful theory of Prandtl comes from considering air as frictionless or inviscid. (29)

At the end of his survey Bairstow returned to this theme and defined his view of the prospects of aerodynamics in terms of this ambiguous and problematic image. We can be assured, he said, that aerodynamics has “a future compa­rable with that in electron theory” (30).

Despite Glauert’s efforts to renegotiate the conceptual distinction between perfect fluid theory and the theory of viscous fluids, it is clear that the lead­ing British mathematical physicists were in no hurry to abandon their view that the distinction was fundamental. The boundary separating the objects of the two theories was treated as ontologically rigid rather than methodologi­cally flexible. Eventually, though, by the mid – and late 1930s, what Glauert called the “true conception of a perfect fluid” appears to have filtered into British mathematical and experimental practice. It was not acknowledged explicitly, but it was implicit in the use of potential irrotational flow as an engineering ideal. By the 1940s its use for this purpose had become routine, for example, in estimating the role played by the viscous boundary layer.98 By this time the circulation theory of lift, and Prandtl’s wing theory, had already become an established part of British aerodynamics. The earlier insistence on a rigid conceptual boundary between ideal and real fluids nevertheless helps to explain why, when Prandtl’s wing theory was finally accepted by the Brit­ish, there was still a note of reservation. Prandtl’s theory may have been, as Bairstow conceded, “the best and most useful working hypothesis of modern times”—but it was still a working hypothesis.

For many years, one of the standard British textbooks in the field was Milne-Thomson’s Theoretical Aerodynamics." The book ran through four editions between 1947 and 1966 and contained the following, revealing obser­vation on the lifting-line theory. Following an explication of Lamb’s contrast between a scheme and a fundamental theory, Milne-Thomson said, “The student should be warned, however, that the investigation on which we are about to embark is one of discussing the deductions to be made from sche – matization of a very complicated state of affairs and that the ‘laws of Prandtl’ which will be used as a basis are not necessarily laws of nature” (191). Con­trasting the Laws of Prandtl with the Laws of Nature was just a picturesque way of saying what most British experts had felt all along. Prandtl’s work on the aerofoil was an exercise in engineering pragmatism rather than a contri­bution to a realistic and rigorous mathematical physics.