Evanescent Viscosity

Glauert’s contribution to the London Congress was a paper titled “Some As­pects of Modern Aerofoil Theory.”96 It covered much of the same ground as the methodological paper given to the RAeS, but with the addition of tech­nical results about propeller theory and wind-tunnel corrections. Though deeply opposed to Bairstow’s view, Glauert did not directly attack what had just been said. Instead he quietly sought to outflank it by demonstrating that the concern with “fundamentals,” as Bairstow conceived it, was out of touch with events at the front line of active research.

Glauert began by pointing out that the study of the forces and moments on a body in motion through a viscous fluid was beset by complexity and prog­ress had been slow. But a “modified form of the classical hydrodynamics” was proving successful. “The present paper,” Glauert went on, “is concerned only with the problem of aerofoil structures, whose essential characteristic is that they give a relatively large lift force at right angles to the direction of motion at the expense of a relatively small drag force retarding the motion” (245). A few minutes earlier Bairstow had drawn attention to the “limited” scope of application of the circulatory theory as a point of criticism and as an unac­ceptable feature of the work of Kutta, Joukowsky, and Prandtl. Right at the outset of his talk Glauert was doing the opposite. He was drawing attention to the limited focus of the work as a wholly-taken-for-granted feature that in no way told against it. Glauert was implicitly making an engineering-style response to Bairstow of exactly the kind that Lanchester had made, explicitly, in the 1915 confrontation.

Having led his audience, nonmathematically, through the main develop­ments in aerofoil theory, Glauert concluded by saying that the most impor­tant feature of the “modern” approach was that it “presents us with a point of view” with which to examine new problems. It provides us with a small number of theoretical conceptions “which serve to bind into a single unity a multitude of experimental results” (255). Clearly this point of view was dif­ferent from that adopted by Bairstow—and Glauert’s idea of unity was not Bairstow’s. For Bairstow unity meant deducibility from the Stokes equations; for Glauert it meant linking experimental results by adopting the modern, methodological standpoint. Glauert expressed himself in an interesting way. Referring to the moment when the boundary layer became infinitely thin, he said, “The effect of the evanescent viscosity is represented in the non-viscous solution by the possibility of a circulation round the aerofoil” (246).

The word “evanescent” means “passing quickly from sight or memory.” It was also the old Newtonian word for describing the infinitesimal quanti­ties that entered into the differential calculus. Infinitesimals were “evanescent quantities” that were neither zero nor nonzero but poised on the very brink of vanishing. Newton and his followers spoke in this way because they did not possess the modern concept of a limiting process.97 Glauert, of course, did possess it. His idea was to contrast the limiting value of, say, /(p) as p ^ 0 with the value of /(0) , that is, the value of the function at p = 0. These can be different. Glauert’s “evanescent viscosity” was thus viscosity on the point of reaching the limit zero, but his language was meant to register a method­ological as well as a mathematical point. It signalizes the difference between deciding that viscosity is zero in step 1 of his three-step methodology, and accepting that it may be treated as zero in step 3.

Bairstow wanted to know why ideal-fluid theory sometimes worked. Glauert’s answer was that it works when the ideal flow is a limiting case of a flow that would take place in a fluid of small viscosity. This answer was not one that Bairstow was prepared to accept. Recall that Bairstow saw no “im­passable barrier” to the idea of a boundary layer, but, he said, difficulties be­gan when the region was said to have an infinitesimal width (244). Bairstow did not want the relationship between inviscid and viscous flows to hinge on a limiting process, and certainly not on a limiting process that was carried out informally. He did not want Glauert’s “evanescent” viscosity; he wanted what, in his own mind, would count as physically real viscosity.98