Introduction
“Turbulence is a physical phenomenon occurring in most fluid flows, and is a major research topic at the cutting edge of science and technology.” This is how the Journal of Turbulence defines its subject matter in 2018. According to its aims and scope, this journal provides
a common venue for communicating advances of fundamental and applied character across the many disciplines in which turbulence plays a vital role. Examples include turbulence arising in engineering fluid dynamics (aero- and hydrodynamics, particulate and multi-phase flows, acoustics, hydraulics, combustion, aeroelasticity, transitional flows, turbo-machinery, heat transfer), geophysical fluid dynamics (environmental flows, oceanography, meteorology), in physics (magnetohydrodynamics and fusion, astrophysics, cryogenic and quantum fluids), and mathematics (turbulence from PDE's, model systems). (Journal of Turbulence 2017)
The Journal of Turbulence was founded in the year 2000. Before the millennium, periodicals like the Physics of Fluids and the Journal of Fluid Mechanics, both established in the mid-1950s, invited contributions on turbulence – and continue to do so. Since 1986 turbulence researchers with quite different disciplinary backgrounds convene every two years for the European Turbulence Conferences (ETC), organized by the European Mechanics Society (EUROMECH). Disciplinary heterogeneity is not novel in this specialty, which meanders between pure and applied research, science and engineering, or however such dichotomies are labeled. In 2011, the editors of a historical account on turbulence, themselves leading representatives of this research field, invited their readers to join them for “A voyage through turbulence” over a hundred-year period from 1880 to 1980 in the company of twelve pioneers who left a mark in this research field: As “scientist and engineer” (Osborne Reynolds), “aerodynamicist and engineer” (Ludwig Prandtl, Theodore von Kármán, Satish Dhawan), “physicist, applied mathematician and engineer” (Geoffrey Ingram Taylor), “meteorologist and mathematician” (Lewis Fry Richardson), “mathematician and statistician” (Andrej Nicolaevich Kolmogorov), “fluid dynamicist” (Stanley Corrsin, George Keith Batchelor, Alan Townsend, Philip Saffman) and “mathematical physicist” (Robert Kraichnan). The disciplinary association was made retrospectively. In the eyes of the editors, the “span of disciplines” reflects how the “problem of turbulence has challenged mathematicians, physicists and engineers alike” (Davidson et al. Reference Davidson, Kaneda, Moffatt and Sreenivasan2011, xii). Ten years earlier, at the occasion of another review, an American and a Russian pioneer of turbulence research concluded that a century of research has amounted to a rough working knowledge to handle with turbulence in many situations, but nothing that could be considered as a comprehensive theory. In this regard “turbulence is still in its infancy. We are naturalists, observing butterflies in the wild” (Lumley and Yaglom Reference Lumley and Yaglom2001, 241). Similar feelings were expressed by Richard Feynman already in the 1960s from the vantage point of a physicist accustomed to clear-cut solutions in classical mechanics. “Today we cannot see whether the water flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders,” he conveyed this message in his famous lectures (Feynman, Leighton, and Sands Reference Feynman, Leighton and Sands1964, 41-12).
While turbulence has long been perceived as a major challenge by engineers and scientists, it has attracted the curiosity of historians of science only recently. In a thorough study of hydrodynamics and hydraulics, Olivier Darrigol exposed the major roots of turbulence research in the nineteenth century (Darrigol Reference Darrigol2002, Reference Darrigol2005). He also pointed to the proverbial gulf between hydrodynamics (as pure science) and hydraulics (as practical engineering) which surfaced with efforts to account for turbulence: “The life of hydrodynamics started with a deplorable contrast between its formal nicety and its empirical impotence” (Darrigol 2008, 230). Turbulence seemed to elude the Euler- and Navier-Stokes equations for ideal (i.e. inviscid) and viscous flows, respectively. By the 1920s, this impotence became reflected in the rhetoric of “the turbulence problem,” as the applied mathematician Fritz Noether titled a review article on the futile attempts to determine the transition from laminar to turbulent flow (Noether Reference Noether1921; Battimelli Reference Battimelli1984; Eckert Reference Eckert2008a, Reference Eckert2010).
At first sight, turbulence may appear to be just another “messy” research field in physics, like solid-state physics, where we are also confronted with a delicate mix of pure and applied research (Martin and Janssen Reference Martin and Janssen2015). Yet turbulence is different, not the least because of the variety of settings in which it emerged, from hydraulic laboratories to aeronautical research facilities. The latter were confronted with wind tunnel turbulence, the former with turbulent pipe flow. Dependent on settings and circumstances, turbulence became a subject of quite different topical discussions (Eckert Reference Eckert2006, Reference Eckert2008b, Reference Eckert2012).
In this paper I describe the emergence of turbulence research in different settings between the two world wars in the twentieth century. Although I focus mainly on German researchers, in particular Prandtl's Göttingen school, their international relations shed light also on the development of the research field at large. I begin with a brief survey of turbulence problems before and during WW I. Next I describe the formation of a community of applied mathematicians, physicists, and “scientific engineers” under the label of Applied Mathematics and Mechanics which provided a loose framework for early turbulence research. In the subsequent sections I follow the major turbulence approaches in their respective settings: boundary layer turbulence; the mixing length approach; experiments on turbulent pipe flow; wind tunnel turbulence and the rise of the statistical theory of turbulence. Finally I provide a brief survey of a turbulence symposium during the international mechanics congress in 1938 in Cambridge MA, at which most contemporary riddles of turbulence were discussed before WW II interrupted the international exchange. In the conclusion I pull the threads together in an effort to portray the interwar period as the crucial phase when turbulence developed into a multi-disciplinary research field.
Turbulence before and during WW I
Most of the research on turbulence in the nineteenth century was motivated by the awareness that there was a gulf between theory and practice concerning the flow of water. The term “turbulence” seems to have been used for the first time by William Thomson (better known as Lord Kelvin) in 1887; but there was no theory of turbulence, and other pioneers of this research field like Joseph Boussinesq, Osborne Reynolds, or Lord Rayleigh seldom used this term. They addressed the motion of water which eluded the established hydrodynamic theory as “tumultuous movements,” “eddy agitations,” “irregular eddies,” or by some other characterization (Schmitt Reference Schmitt2017). At the turn from the nineteenth to the twentieth century, the gulf between theory and practice in fluid mechanics reached its climax. Wilhelm Wien, then a theoretical physicist and renowned expert on hydrodynamics, introduced a textbook on this subject with the observation that practical applications were to such an extent beyond the reach of theory that engineers adopted their own procedure to deal with hydrodynamical problems, “which is usually called hydraulics” (Wien Reference Wien1900, iii). Hydraulics, in contrast to hydrodynamics, was an engineering discipline in the realm of technical mechanics. In Germany it was taught at technical colleges (technische Hochschulen) rather than universities and disposed of its own textbooks (e.g. Föppl Reference Föppl1898). The renowned Enzyklopädie der mathematischen Wissenschaften assigned hydrodynamics and hydraulics to different authors (Love Reference Love1901; Forchheimer Reference Forchheimer1905). From the perspective of theoretical physics, hydraulics lacked “so much of a strict method, in its foundations as well as in its conclusions, that most of its results do not deserve a higher value than that of empirical formulae with a very limited range of validity” (Wien Reference Wien1900, iii).
The culprit was turbulence. “Hydraulics is concerned with different laws for the resistance,” Heinrich Blasius said in 1908, in a talk on turbulent flows – which by that time was mainly concerned with the flow of water in pipes and channels (Blasius Reference Blasius1908). The talk was part of a seminar on hydrodynamics organized by the Göttingen mathematician Felix Klein together with Ludwig Prandtl and Carl Runge, both directing the university's new institute for applied mathematics and mechanics, and the geophysicist Emil Wiechert. Blasius had just finished a doctoral dissertation under Prandtl on boundary layer theory. In his seminar presentation he reviewed the most recent results of research on turbulence. He discerned two main problems: transition from laminar to turbulent flow and fully developed turbulence. For the former, he referred in particular to the work of Reynolds (Launder and Jackson Reference Launder, Jackson, Davidson, Kaneda, Moffatt and Sreenivasan2011), for the latter to Boussinesq (Darrigol Reference Darrigol2002) who considered turbulent friction as an additional viscosity due to vortical motion (eddy viscosity). Blasius characterized Boussinesq's approach as “hydraulic.”
At the same time Arnold Sommerfeld, a former assistant of Felix Klein with a keen interest in displaying his skills in theoretical physics (then in the fledgling stages to become a discipline in its own right), reacted to the challenge of turbulence (Eckert Reference Eckert2013). He focused on the special case of plane Couette flow, i.e. a flow between two parallel walls, one at rest, the other moving at constant speed. Sommerfeld named on this occasion the dimensionless constant R = ρ U h / μ (ρ = density of the fluid, U = velocity of the moving wall, h = distance between the walls, μ = viscosity of the fluid) the Reynolds number (Rott Reference Rott1990). He attempted to derive a critical Reynolds number at which the laminar flow becomes unstable and gives rise to turbulence. By then “hydraulic” became almost a label for turbulent flow. “At small R the flow follows the simple hydrodynamic laws, i.e. it is laminar,” Sommerfeld's student Ludwig Hopf wrote in his doctoral thesis on “Turbulence in a River” in 1909, “at large R there arise so-called turbulent motions which are characteristic for the hydraulic state” (Hopf Reference Hopf1910, 803). In the following years, Hopf and other theorists made every endeavor to accomplish Sommerfeld's approach with the derivation of a critical Reynolds number, but their efforts failed completely. The same approach was introduced independently already in 1907 by the Irish mathematician William McFadden Orr, but it became widely known only in the 1920s. According to this “Orr-Sommerfeld approach” plane Couette flow would always remain laminar – in obvious contrast to the empirical observation that any flow becomes turbulent at a sufficiently large Reynolds number (Eckert Reference Eckert2010).
While turbulent flow in the nineteenth and early twentieth century was associated mainly with the “hydraulic” flow of water in pipes and channels, the advent of aeronautics added new settings for investigating turbulence. The giant Zeppelins called for studies of the drag which such monsters experienced in free flight. In 1907 the entrepreneurial mathematician Klein perceived aeronautics – and that meant mainly the flight of airships – as an opportunity to establish aerodynamics as another applied specialty at Göttingen University. Prandtl was charged with the establishment of a new facility for model studies of motorized airships (Motorluftschiffmodell-Versuchsanstalt, MVA). It was dedicated to wind tunnel measurements of airship models, aiming at shapes with minimal air resistance. With the advent of airplanes, the scope of this facility extended to wind tunnel measurements on airfoils, propellers, and other parts of airplanes. In WW I it was turned into a big research establishment with a broad range of tasks, from the study of lift and drag of aerofoils to the aerodynamics of bombs or the noise of submarines due to cavitation on propeller blades. The Aerodynamische Versuchsanstalt (AVA), as the larger facility was renamed in 1919, disposed of a new wind tunnel of considerable size and was by then the world's largest aeronautical research establishment (Rotta Reference Rotta1990).
Already in the first wind tunnel of the MVA, turbulence made an appearance in the form a phenomenon that had gone unnoticed in water flows. In 1912, a blatant discrepancy for the air resistance of spheres occurred when Prandtl compared the measurements from the Göttingen wind tunnel with those from Gustave Eiffel's wind tunnel in Paris which was operated at higher air speeds. According to Eiffel's measurements, the drag coefficient of a sphere would suddenly decrease at higher speeds! At first Prandtl and his collaborators thought that Eiffel had omitted a factor of 2, but Eiffel insisted in the correctness of his measurements. By inserting a constriction into the Göttingen wind tunnel, Eiffel's measurements finally were confirmed. At a critical air speed the drag coefficient dropped to a much lower value. Prandtl suggested an explanation of this phenomenon in terms of his boundary layer concept: When the initially laminar boundary layer around the sphere becomes turbulent beyond a critical air speed, it entrains air from the wake behind the sphere so that the boundary layer stays attached to the surface of the sphere longer than in the laminar case. Hence the onset of turbulence in the boundary layer reduces the wake behind the sphere and thus also its drag. The boundary layer concept, which had been applied so far to laminar flow only, thus became extended to turbulent flow. In 1914 Prandtl and his assistant, Carl Wieselsberger, demonstrated this turbulence effect with a thin “trip wire” around the sphere which made the flow in the boundary layer behind the wire turbulent. The extension of the wake was made visible with smoke. Thus it was obvious that the trip wire reduced the wake, and therefore also the air resistance (Rotta Reference Rotta1990, 83–85; Bodenschatz and Eckert Reference Bodenschatz, Eckert, Davidson, Kaneda, Moffatt and Sreenivasan2011, 45–46; Bloor Reference Bloor2011, 253; Eckert Reference Eckert2017, 88–91).
This turbulence effect was not confined to spheres. It concerned all bodies in a stream of air whose drag was dominated by their shape (“form drag”), such as bombs and shells. Airplanes were affected by this phenomenon in a peculiar way because the wings of a biplane – the most common type of airplane in WW I – were held together by struts and wires which experienced the same turbulence effect depending on their shape. If the turbulence-induced transition from high to low drag happened during lift-off or landing, a pilot would get into trouble. Thus turbulence emerged as a research subject in a military context. Of course, this was merely a minor part within the surge of aeronautical studies motivated by WW I and should be considered within the entire war effort of Imperial Germany. Funded by the Navy and War Ministry, the MVA was turned from a small research laboratory into a big-science facility between 1915 and 1918. By the end of WW I, Prandtl was in charge of the largest aeronautical research facility in the world. Disregarding the outcome of the war, Prandtl and his Göttingen wind tunnel facility were widely admired as role models for applied aerodynamics.
With turbulence becoming the subject of war contracts, it is not astonishing that the fundamental physics of turbulent flow received new interest. In 1916 Prandtl sketched “A working program for a theory of turbulence.” Like Blasius in his presentation in Klein's seminar, Prandtl discriminated between the onset of turbulence and fully developed turbulence as the two pillars of this research program. “Statistical equilibrium of a set of vortices in an ideal fluid in the vicinity of a wall,” he noted for example as one topic for future research. He imagined that the boundary layer sheds vortices from the wall into the fluid and that the turbulent flow at some distance from the wall results from a balance between the vortex creation at the wall and the vortices destroyed in the fluid as a result of friction (Bodenschatz and Eckert Reference Bodenschatz, Eckert, Davidson, Kaneda, Moffatt and Sreenivasan2011, 47–48). With hindsight we may discern here the root for Prandtl's turbulence research in the interwar period. But we have to turn to the institutional developments in Germany after WW I in order to place this research in its appropriate context which far extended the framework of aeronautics.
After WW I: The Formation of a New Umbrella for Turbulence Research
Before the war, the annual meetings of the Gesellschaft Deutscher Naturforscher und Ärzte (GDNÄ) provided the only opportunity for applied mathematicians, physicists, and engineers in German speaking countries to express common concerns. When they met again for the first time after the war in 1920 in Bad Nauheim, Prandtl and others who perceived their experience from the war as a lesson for the future, expressed the need for a new umbrella for application-oriented sciences. At the same time, “technical” physicists mainly from industrial laboratories formed a new society, the Deutsche Gesellschaft für Technische Physik (DGTP), in close association with the older Deutsche Physikalische Gesellschaft (DPG). In September 1921, these two physical societies held a joint meeting with the Deutsche Mathematiker-Vereinigung (DMV) in Jena. At this occasion “for the first time, applied mathematics and mechanics was coming to its own to a larger extent,” as the new journal Zeitschrift für angewandte Mathematik und Mechanik (ZAMM) proclaimed in its first volume (ZAMM 1921, 419). The journal propagated the common goals of Prandtl and his former disciple Theodore von Kármán, who now directed his own institute for aerodynamics at the Technische Hochschule Aachen, Richard von Mises and Hans Reissner, professors at the Technische Hochschule Berlin for applied mathematics and mechanics, respectively. They regarded applied mathematics and mechanics as a specialty for which there did not yet exist an appropriate organizational umbrella. The result of their collaborative effort was, besides the foundation of the ZAMM, the establishment of a new professional society, the Gesellschaft für angewandte Mathematik und Mechanik (GAMM) (Gericke Reference Gericke1972, 5–10; Tobies Reference Tobies1982).Footnote 1
The label “applied mathematics and mechanics” reflects an identity of this group that was different from “technical physics,” represented mainly by physicists working in industry (Hoffmann Reference Hoffmann, Guntau and Laitko1987). Besides fluid mechanics, applied mechanics comprised plasticity, elasticity, and strength of materials. These were also the topics at an international meeting in 1922 in Innsbruck, Austria, which was convened largely at the initiative of Kármán and the Italian mathematician Tullio Levi-Civita who had been appointed in 1920 to the chair of mechanics at the University of Rome. In the tense political climate after the war, the success of the rather unofficial Innsbruck meeting encouraged Kármán and other representatives of this new specialty to establish international congresses of applied mechanics on a regular basis. The first such event took place in 1924 in Delft, Netherlands. The subsequent international mechanics congresses were convened in Zurich (1926), Stockholm (1930), Cambridge, UK (1934) and Cambridge, MA (1938) – with ever growing international participation and official recognition (Battimelli Reference Battimelli and Juhasz1988, Reference Battimelli, Gagliasso and Battimelli1992, Reference Battimelli1996).
By the mid-1920s, after the meetings in Jena, Innsbruck, Delft, and Zurich, it was obvious that a new international community of applied mathematicians, “scientific engineers” (a notion coined by Prandtl), and physicists had surfaced. Its representatives were scientists of international reputation like Levi Civitá (Italy), Johannes Martinus Burgers (Netherlands), Geoffrey Ingram Taylor (Great Britain), Joseph Kampé de Fériet (France) or Hugh Dryden (USA), to name only some who left a mark in the history of turbulence. The label of applied mechanics and mathematics attributed to them a distinct orientation, disregarding the affiliation with their mother disciplines physics, mathematics, or engineering which remained unaffected by the new umbrella. The International Congress for Applied Mechanics was the event where they met their true peers; this was the framework in which most research on turbulence in the interwar period was nurtured.
Turbulence in the Boundary Layer
Already at the Jena meeting in 1921, turbulence was in the spotlight of discussions between physicists, mathematicians, and engineers. Prandtl presented some results of his student Oskar Tietjens with which they hoped to explain the onset of turbulence without running into the deadlock of Sommerfeld's method (which did not yield a critical Reynolds number for the stability of laminar Couette flow, see Eckert Reference Eckert2010). Because turbulence occurs at high Reynolds numbers they approached this problem from the limit of inviscid flow (where the Reynolds number is infinite) which had been studied in great detail by Lord Rayleigh in the 1880s (Darrigol Reference Darrigol2008, chap. 5.5). In contrast to Sommerfeld's case of plane Couette flow between two plane walls, Prandtl and Tietjens had the flow in the laminar boundary layer along a flat plate in mind which at some distance from the plate could be regarded as a free inviscid flow. But if the “turbulence problem” in Sommerfeld's approach was the impossibility of unstable wavelike disturbances, in the Prandtl-Tietjens approach it was the opposite: any disturbance would render the laminar flow unstable. “We did not quite believe this result at first and checked it three times by independent and different methods,” Prandtl presented this outcome at Jena. “Each time it resulted in the same sign, which means instability.” The problem provoked controversial debates as testified by the conference proceedings and the ensuing correspondence of Prandtl, Noether, and others. It was solved only in 1929 by another student of Prandtl, Walter Tollmien, who arrived in his doctoral dissertation at a stability diagram which showed how a set of unstable oscillations reaches like a tongue from high to low Reynolds numbers into a sea of stable oscillations (Eckert Reference Eckert2006, 114–116).
While Prandtl aimed at a theory for the transition from laminar to turbulent flow in the boundary layer, his former student Kármán conceived a theory for the boundary layer in a state of fully developed turbulence. “Dear Master, colleague, and former boss,” he began a five-page letter to Prandtl in which he sketched “a kind of ‘turbulent boundary layer theory’.”Footnote 2 Kármán derived a formula for the velocity profile U in the turbulent boundary layer as a function of the distance y from the wall: U proportional to y 1/7. He recalled that Prandtl had mentioned this result earlier, but could not remember how Prandtl had derived it and whether it was already published. Prandtl responded that he was going to elaborate it only later and that Kármán should feel free to publish it. Kármán submitted an extended version of the theory to the ZAMM where he combined his derivation with general considerations about boundary layers. “In order to expose the physical meaning of the boundary layer theory” he elaborated a method to compute laminar and turbulent boundary layers from the balance of momentum in the boundary layer (Kármán Reference Kármán1921). It became clear also why Kármán designated his considerations only as “a kind of ‘turbulent boundary layer theory’.” Turbulent features were not derived from first principles, but empirical findings. The y 1/7-law for the turbulent velocity profile was based on the empirical law of turbulent pipe flow established by Blasius in 1913, that the loss of pressure per unit length varies like U7 /4.
Nevertheless, next to other papers on turbulence in ZAMM like Fritz Noether's article on the “turbulence problem,” Kármán's “theory” transmitted to the readers of this journal the message that turbulence provided a challenge that was worth further efforts. The meetings in Innsbruck and in Delft offered Kármán the opportunity to elaborate one or another aspect for a theory of turbulence (Kármán Reference Kármán, von Kármán and Levi-Cività1924, Reference Kármán, Biezeno and Burgers1925; Leonard and Peters Reference Leonard, Peters, Davidson, Kaneda, Moffatt and Sreenivasan2011, 105). As he recalled many years later, this was the period when he and others began “to believe that turbulent motion could eventually be subjected to mathematical law.” The quest for such a law turned into a rivalry with Prandtl. “I came to realize that ever since I had come to Aachen my old professor and I were in a kind of world competition. The competition was gentlemanly, of course. But it was first-class rivalry nonetheless, a kind of Olympic games, between Prandtl and me, and beyond that between Göttingen and Aachen. The ‘playing field’ was the Congress of Applied Mechanics. Our ‘ball’ was the search for a universal law of turbulence” (Karman Reference Kármán1967, 135). As the rivalry unfolded it became clear that there was as much intrinsic interest in solving that problem as in the technological prospects of a universal formula.
The Mixing Length Approach
In March 1925 Prandtl reported at a meeting of the GAMM in Dresden about his recent “investigations on fully developed turbulence” (Prandtl Reference Prandtl1925; Battimelli Reference Battimelli1984, 83–86). He focused on Boussinesq's eddy viscosity ε which plays an analogous role as the kinematic viscosity ν for the viscous shear stress. Because the dimension of the eddy viscosity, like that of the kinematic viscosity, is length times velocity, Prandtl suggested to regard the length l as a “braking length” or “mixing length” for a turbulent “bale of fluid” moving at a mean velocity and exchanging momentum until it becomes mixed in other turbulent eddies. At first look he only replaced the unknown quantity ε by another unknown quantity l. But in contrast to the eddy viscosity ε the mixing length l was amenable to adjustments in specific cases. Prandtl illustrated this approach with the case of a jet of turbulent air that is blown through a nozzle in the ambient air at rest. By the assumption that the mixing length is proportional to the width of the broadening jet it was possible to solve the differential equation for the mean turbulent velocities in the jet behind the nozzle. Their theoretical distribution was in excellent agreement with experimental measurements.
Prandtl presented this approach in more detail in 1926 at a conference on “Hydraulic Problems” in Göttingen and at the Second International Congress for Applied Mechanics in Zurich. “The effect of Prandtl's paper on me was immediate. I suddenly felt that Prandtl had won a round,” Kármán recalled his reaction (Karman Reference Kármán1967, 135). Prandtl, however, hesitated to praise his approach as a break-through. It is “far from being something accomplished,” he dampened the expectations of his colleagues. “The investigations concerning turbulence with which we are dealing in Göttingen since about five years have diminished unfortunately the hope for a deeper understanding of the inner mechanisms of turbulent flow” (Prandtl Reference Prandtl and Meissner1927, 62). Although the approach could be used to compute the “free turbulence” of broadening jets ejected through nozzles, or of wakes behind obstacles, Prandtl found it difficult to apply it to the turbulence along a wall. In order to recover the y 1/7-law for the turbulent velocity distribution at a distance y from the wall, assumptions for the mixing length had to be made which lacked the plausibility of the mixing length approach in free turbulence. Based on recent measurements, however, the y 1/7-law appeared less certain at higher Reynolds numbers (Prandtl supposed that the exponent became 1/8, then 1/9 with growing Reynolds number). But this change could not make the mixing length more plausible.
By 1929 new measurements on pipe flow at very high Reynolds numbers by Johann Nikuradse, another doctoral student of Prandtl, suggested a logarithmic formula instead of a power law for the turbulent velocity distribution with growing distance from a wall. When Kármán learned about these measurements, he modified Prandtl's mixing length approach. The idea for this modification came from an experimental study in his Aachen institute of turbulent channel flow with different wall surfaces: at the centre-line of the channel, the velocity profiles lined up with each other if they were shifted parallel. From this observation, Kármán concluded that at some distance from a wall the velocity fluctuations are similar anywhere and anytime in fully developed turbulent flow. Unlike Prandtl, he introduced the mixing length l as the characteristic scale of the fluctuating velocities determined by l = k U'/U'', where k is a dimensionless constant and U', U'' are the first and second derivatives of U with respect to y. When he used this mixing length in the formula for turbulent shear stress, he arrived at a logarithmic velocity distribution and a logarithmic formula for the turbulent friction coefficient (Kármán Reference Kármán1930).
Unlike Prandtl's approach with more or less plausible assumptions about the mixing length, Kármán's similarity concept involved only the constant k which was independent from the specific flow under consideration. “Kármán's constant,” as k became labelled, represents a universal feature of turbulence. “I told Prandtl I had something new to report, and he invited me to make my presentation before the Göttingen Scientific Society,” Kármán recalled this round of their competition. After Kármán's presentation “Prandtl was crestfallen” and “chagrined” that his former pupil had once more succeeded “in exercising his well-known talent for skimming the cream off the milk” (Kármán Reference Kármán1967, 137–138). A few months later, Kármán presented his theory at the Third International Congress of Applied Mechanics in Stockholm. “The resistance law [for a smooth wall] is no power law,” he alluded to the earlier efforts of Prandtl and himself about the 1/7th law. He presented a diagram about the plate skin friction where he compared the “Prandtl v. Kármán Reference Kármán1921” theory with the “new theory” and with recent measurements from the Hamburgische Schiffbau-Versuchsanstalt, a facility dedicated to practical concerns in naval architecture. “It appears to me that for smooth plates the least mismatch between theory and experiment has disappeared,” Kármán concluded his Stockholm presentation (Kármán Reference Kármán, Oseen and Weibull1931).
Prandtl swiftly confirmed Kármán's results. He did not start from a similarity hypothesis but from a generalized presentation of experimental data. In contrast to Kármán's elaboration of theoretical foundations, Prandtl framed his publication in the form of an introduction to the presentation of new data in the forthcoming Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen, the series of his laboratory communications. He duly acknowledged Kármán's earlier publications from the year 1930, but he claimed that he had arrived at the same results “at a time when Kármán's papers had not yet been known, so that once more, like ten years ago with the same problem, the thoughts in Aachen and Göttingen followed parallel paths” (Prandtl Reference Prandtl1932).
In May 1932, the Hamburgische Schiffbau-Versuchsanstalt convened a conference where the recent theories and experiments about turbulent friction were reviewed. Kármán was invited for a talk on the theory of fluid resistance, but he could not attend in person so that his paper was read by another attendee. Franz Eisner, an engineer from the Preussische Versuchsanstalt für Wasserbau und Schiffbau in Berlin, addressed the same theme from a broader perspective, and Günther Kempf from the Hamburgische Schiffbau-Versuchsanstalt presented recent results about friction on smooth and rough plates. Prandtl and others were invited to present commentaries and additions. By and large, this conference served to acquaint practitioners, particularly engineers in naval architecture, with the recent advances achieved in the research laboratories in Göttingen, Aachen, and elsewhere (Kempf & Foerster Reference Kempf and Ernst Foerster1932).
Two months after this conference, the Schiffbautechnische Gesellschaft published short versions of these presentations in its journal Werft, Reederei, Hafen. From Eisner's presentation a diagram about plate resistance was shown which characterized the logarithmic law “after Prandtl (Ergebnisse AVA Göttingen, IV. Lieferung Reference Prandtl1932)” as the best fit of the experimental values (Eisner Reference Eisner1932). According to this presentation, an “interregnum of power laws” lasted until Prandtl formulated the correct logarithmic law. When Kármán saw this article he was upset. He felt that his breakthrough was ignored. From this report about the Hamburg conference “it looks as if I had given up work on this problem after 1921,” he complained in a letter to Prandtl, “and that everything has been done in 1931/32 in Göttingen.” He asked Prandtl to correct this erroneous view. “I write so frankly how I think in this matter because I know you as the role model of a just man,” he appealed to Prandtl's fairness. But he had little sympathy for “your lieutenants who understandably do not know other gods beside you. They wish to claim everything for Göttingen.”Footnote 3 What makes this rivalry so peculiar is the emphasis on practice. Although Kármán's priority was evident from his publications in 1930, Kármán insisted that it was also acknowledged in the Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen because this was widely regarded as the “standard for practitioners.”Footnote 4
Although Prandtl acknowledged Kármán's priority, and both exchanged conciliatory letters, the controversy left traces. Kármán, who had moved in 1933 permanently to the USA, used the first opportunity to present his own version of “Turbulence and Skin Friction” in the first issue of the new Journal of the Aeronautical Sciences (Kármán Reference Kármán1934). Similarly, Prandtl's “lieutenant” Hermann Schlichting vigorously propagated the Göttingen viewpoint in his textbook Boundary Layer Theory, which became the international standard for the engineering community; it emerged from wartime lectures in 1941–42 that were translated into English soon after the war (Schlichting Reference Schlichting1949, Reference Schlichting1951).
Pipe Flow between Physics and Engineering
It is not accidental that Kármán regarded the practitioners as his true addressees. Prandtl also presented reviews of the current state of turbulence research mainly in engineering journals (e.g. Prandtl Reference Prandtl1933). There was no clear-cut separation of theory versus practice in the sense that the former was addressed to academic and the latter to engineering journals. Kármán's and Prandtl's theoretical efforts were largely based on experimental data. As long as Blasius's empirical formula for the resistance in turbulent pipe flow was taken for granted, they aimed at a theoretical derivation of the “1/7th-law.” When Nikuradse's pipe flow measurements at very high Reynolds numbers made a logarithmic law seem more appropriate, Kármán and Prandtl modified their earlier approaches accordingly. The validation of one or another theory was sought in diagrams for the friction coefficient as a function of the Reynolds number, most often derived for the flow of water through a pipe.
While these data showed more or less agreement with theoretical curves at very high Reynolds numbers where the turbulence was fully developed, and perfect agreement at very low Reynolds numbers in the regime of laminar flow, the transition region from laminar to turbulent flow was beyond the reach of theory. Laminar pipe flow was characterized by the well-known parabolic Poiseuille flow profile. Werner Heisenberg had analyzed in his doctoral thesis under Sommerfeld the stability of plane Poiseuille flow and derived a limit of stability (Heisenberg Reference Heisenberg1924), but his procedure was disputed (Noether Reference Noether1926). When Theodor Sexl, a theoretical physicist from Vienna, applied the Orr-Sommerfeld approach to three-dimensional Poiseuille flow, he found no instability (Sexl Reference Sexl1927). Thus theory was in the same deadlock as in the case of plane Couette flow.
Experimental studies on the transition to turbulence of laminar pipe flow also could not resolve this issue. The critical Reynolds number for the onset of turbulence varied considerably from experiment to experiment. Ludwig Schiller, an experimental physicist from Leipzig University who focused his investigations in the 1920s on pipe flow measurements, reported critical Reynolds numbers in the range from several hundreds to ten-thousands, depending on the inflow into the pipe. At low Reynolds numbers he observed the formation of vortex rings and an intermittent turbulent flow (Schiller Reference Schiller1932, 135–138). Schiller's investigations entailed a number of precision measurements on pipe and channel flow by his pupils. Alexander Naumann observed in his doctoral thesis on the onset of turbulence in pipe flow “a kinship between the inflow in a pipe and the flow around a bluff body. Both display the same characteristic flow pattern: laminar flow, vortex street, turbulence” (Naumann Reference Naumann1931, 98). Hermann Kurzweg published in 1933 the results of investigations in which he further analyzed the vortex street that preceded the onset of turbulence (Kurzweg Reference Kurzweg1933). With these studies Schiller and his group at the Institute of Physics of Leipzig University made themselves a name as a center of experimental research on turbulence.
The fact that theoretical physicists like Heisenberg and Sexl aimed at a theory for the transition to turbulence, and that experimental physicists like Schiller reviewed the experimental aspects in the Handbuch der Experimentalphysik, could make us believe that turbulence was an important item on the agenda of physics. Both for Heisenberg and Sexl, however, these studies were rather brief excursions from their main research in quantum and nuclear physics. Schiller, too, was rather exceptional with his focus on pipe flow. Officially he was the head of a Division of Applied Mechanics and Thermodynamics within the Institute of Experimental Physics directed by Peter Debye. But when Schiller asked the dean of his faculty in a memorandum to promote his unit to the rank of an institute, he met with strong opposition. With the consent of Debye and Heisenberg, the directors of the Leipzig University Institutes for Experimental and Theoretical Physics, the dean argued that Schiller's specialty does not fit quite well to a university but rather to a Technische Hochschule. “Professor Debye, with whom I had discussed these questions regarding Schiller's memorandum, shares this view, and Heisenberg also.”Footnote 5 In other words, Schiller should get such ambitions out of his head and be happy that his research was tolerated under the roof of a university.
With the advent of quantum mechanics and revolutionary breakthroughs in nuclear physics (1932 was labelled the “annus mirabilis” of nuclear physics), many physicists regarded the study of turbulent flow in water pipes less rewarding than the investigation of atoms and elementary particles. Physicists like Geoffrey Ingram Taylor, who had focused their own research to fluid mechanics, clearly expressed discomfort with this situation. Taylor felt “very strongly,” as he wrote in a letter to Prandtl in 1935, “that if the Nobel Prize is open to non-atomic physicists it is definitely insulting to us that our chief – and I think that in England and USA at any rate means you – should never have been rewarded in this way.”Footnote 6 Prandtl fostered “no hopes in this direction,” he responded to Taylor, because applied mechanics had attained the status of a separate discipline besides physics, at least in Germany. “If the Swedes categorize science in the same way as we do it here then I will come as little into consideration as mathematicians and could therefore console myself as the mathematicians do.”Footnote 7
Prandtl's situation was even more unique because he was head of a Kaiser-Wilhelm-Institute (KWI) dedicated to research in fluid dynamics. His KWI for Fluid Dynamics (“Strömungsforschung”) was established in 1925 next to the Aerodynamische Versuchsanstalt (AVA) in Göttingen in order to prevent him from accepting a call to the technische Hochschule in Munich. Directing a KWI was a most prestigious position and granted Prandtl the freedom and means to choose his research subjects beyond mere considerations of utility like at the AVA, so that he could focus in his research on more or less fundamental aspects as he deemed it appropriate. This makes it difficult to qualify his research on a scale from “pure” on the one end to “applied” on the other.
Wind Tunnel Turbulence
The exchange between Prandtl and Taylor on the Nobel prize was preceded by an extensive correspondence on turbulence. Like Prandtl and Kármán, Taylor regarded turbulence as the ultimate challenge of fluid mechanics. Although the onset of turbulence was still an unsolved problem, their focus was by now on fully developed turbulence – not the least because experimental techniques had been advanced so that velocity fluctuations could be measured from point to point in a turbulent flow field. Thus the statistical properties of fully developed turbulent flow, which had eluded theoretical investigations such as the mixing-length approach, became the subject of experimental and theoretical studies. New experimental investigations at the National Physical Laboratory (NPL) revealed that fully developed turbulent pipe flow was isotropic near the center of the pipe, i.e. the ratio of the velocity fluctuation u/U, v/U and w/U was equal, where U is the mean flow velocity along the centerline of the pipe and u, v, w are the velocity disturbances along three orthogonal axes (Fage and Townend Reference Fage and Townend1932). At the same time, physicists at the National Bureau of Standards (NBS) in Washington, D.C., brought hot-wire techniques to perfection for recording electronically velocity fluctuations in the air-stream of wind tunnels (Dryden et al. Reference Dryden, Schubauer, Mock and Skramstad1936). At the NPL, too, the measurement of wind tunnel turbulence by hot-wire techniques was becoming a major research effort (Simmons and Salter Reference Simmons and Salter1934, Reference Simmons and Salter1938). “I lately have been doing a great deal of work on turbulence,” Taylor informed Prandtl in March 1935 about a study in which he compared his theoretical results with hot-wire measurements of wind tunnel turbulence at the NPL and the Bureau of Standards in the USA.Footnote 8 He published his “Statistical Theory of Turbulence” in an extraordinary sequence of papers in the Proceedings of the Royal Society (Taylor Reference Taylor1935, Reference Taylor1936, Reference Taylor1938) which marked a “turning point” (Battimelli Reference Battimelli1984, 92; Reference Battimelli1986, S24) in the history of turbulence.
Prior to hot-wire measurements, spheres served as indicators for the degree of turbulence in the airstream of a wind tunnel. “The determination of turbulence is now a routine matter in many wind tunnels,” Dryden and his collaborators reviewed the state of the art for measuring wind tunnel turbulence, “the most common method being that of determining the value of the Reynolds Number of a sphere for which the drag coefficient is 0.3, the so-called critical Reynolds Number” (Dryden et al. Reference Dryden, Schubauer, Mock and Skramstad1936, 109). At the critical Reynolds number of a sphere (due to the turbulence effect on the sphere drag discovered by Eiffel and analysed by Prandtl in 1914) the drag coefficient changed from about 0.5 to 0.1. The lower the critical Reynolds number, the higher the degree of turbulence in the airstream of the wind tunnel. With the hot-wire technique, a more direct measurement of turbulence was possible in terms of velocity fluctuations, and Taylor's statistical theory provided the tools for turning these measurements into expressions for the intensity and the scale of turbulence in a wind tunnel. From the velocity fluctuations measured at two locations separated by a distance y a correlation coefficient R(y) and a typical length 
$L = \smallint R( y )dy$ may be computed. L represents a length scale for the turbulence. It may roughly be interpreted as the mean size of turbulent eddies. The ratio between the root-mean-square of the fluctuating velocity to the speed of the airstream was considered as the intensity of turbulence (Dryden et al. Reference Dryden, Schubauer, Mock and Skramstad1936).
Prandtl had also begun to introduce hot-wire techniques in his laboratory. Together with his collaborator Hans Reichardt he published in 1934 the results of measurements in a wind tunnel with a rectangular cross section (100 cm x 25 cm) which displayed the correlation of turbulent velocity fluctuations at different positions (Prandtl and Reichardt Reference Prandtl and Reichardt1934). Taylor reproduced these results, among others, as corroboration of his theory (Taylor Reference Taylor1935, 456). “Your paper with Dr. Reichardt shows me once again how difficult it is to suggest to people research work that is worth doing and yet has not been tried at Göttingen,” Taylor admired the research program on turbulence that Prandtl was pursuing at the KWI in Göttingen.Footnote 9
A Symposium on Turbulence
Prandtl's central role and the growing importance of research on turbulence is also illustrated by a decision at the Fourth Congress of Applied Mechanics in Cambridge in 1934 to organize at the next Congress a special symposium on turbulence chaired by Prandtl. The suggested symposium was supposed to be “not only the principal feature of this Congress, but perhaps the Congress activity that will materially affect the orientation of future research” (Hunsaker and Kármán Reference Hunsaker, von Kármán, Hartog and Peters1939, xvii).
For scientists from Nazi Germany participation in international congresses was not only a matter of scholarly merits. By 1938 “non-Aryan” scientists have been dismissed from their academic positions and largely excluded from participation in their professions – which also extended to conferences. International congresses, in particular, became subject to political meddling. The German participants at the Fifth Congress of Applied Mechanics in Cambridge MA were grouped as a delegation under the leadership of Prandtl who was advised by the Deutsche Kongress-Zentrale, a sub-organisation of the propaganda ministry, to care for appropriate behavior abroad.Footnote 10 Preparations began many months before the congress. “We have arranged to have the Congress brought to the attention of the German Ambassador in Washington with the request that the German Government consider the adequacy of their scientific representation at the Congress,” the Congress Secretary informed Prandtl in November 1937 about the political steps undertaken so far in the United States. With regard to the scientific preparations, he noted that Taylor had already accepted the invitation to present the general lecture on turbulence. He asked Prandtl to correspond with “Taylor, Burgers, and other men interested in turbulence” regarding the further organization of the turbulence symposium.Footnote 11
The names of the participants in this symposium indicate the disciplinary and institutional heterogeneity of turbulence research in the 1930s. Burgers had started his career in quantum physics as a doctoral student of Paul Ehrenfest before he became Professor in the Department of Mechanical Engineering, Shipbuilding and Electrical Engineering at the Technical University in Delft, where he founded the Laboratory of Aero- and Hydrodynamics. Carl-Gustaf Rossby was a meteorologist and expert on atmospheric turbulence, with affiliations to the US Weather Bureau, the Aeronautics Department of the Massachusetts Institute of Technology (MIT) and the Woods Hole Oceanographic Institution. Their home institutions underscore the impression of a multifaceted and international research field: the Kaiser-Wilhelm-Institut (KWI) für Strömungsforschung (Prandtl, Tollmien, F. Schultz-Grunow), the Guggenheim Aeronautical Laboratory of the California Institute of Technology (GALCIT) (Kármán, Clark Millikan), Cambridge University (Taylor), Leipzig University (Ludwig Schiller), the National Bureau of Standards (NBS) (Dryden and his collaborators), the Scripps Institution of Oceanography (Harald Ulrik Sverdrup), Lille University (Joseph Kampé de Fériet), the MIT (Norbert Wiener) or the National Advisory Committee for Aeronautics (NACA) (Eastman N. Jacobs, A. E. von Doenhoff) and others. As a reviewer of the conference proceedings observed for Nature, among sixty-two papers in the section on fluid mechanics twenty-four dealt with turbulence. He picked out Wiener's contribution on “The Use of Statistical Theory in the Study of Turbulence” in order to illustrate how far turbulence research could be regarded as a mathematical challenge: “Behind the seeming innocence of this title there lies in this paper the beginning of a more general and systematic method of attacking the important problem of turbulence. The basic theorem is an extension by Wiener of the original ergodic theorem of Birkhoff” (Nature 1939).
On the other side, Taylor's, Prandtl's, and Dryden's papers pointed to the more mundane problems of measuring turbulence and making sense of one or another set of data. Prandtl, for example, presented slides from the turbulent motion behind a grid drawn through quiet water – an alternative to hot-wire measurements behind grids in wind tunnels for the study of isotropic turbulence. He visualized the flow pattern at various distances from the grid with iron-glance flakes which aligned in the region of large shear stress. Thus he established a relation between the size of turbulent eddies and the distance downstream from the grid which could be compared with results from Taylor's statistical theory of isotropic turbulence (Prandtl Reference Prandtl, Hartog and Peters1938). Dryden presented recent hot-wire measurements of grid-generated wind tunnel turbulence from which the “spectrum of turbulence” could be determined. Measuring the contribution of eddies of different size provides a “somewhat more detailed picture of turbulent motion,” Dryden praised this progress in hot-wire measurement technique (Dryden Reference Dryden, Hartog and Peters1938, 363).
By and large, the symposium exposed more problems with turbulence than solutions. In retrospect it contained the seeds for major breakthroughs (Bodenschatz and Eckert Reference Bodenschatz, Eckert, Davidson, Kaneda, Moffatt and Sreenivasan2011, 70), but from a contemporary perspective it was less satisfactory. As the Russian pioneer of aerodynamics Dimitri Riabouchinsky observed in the discussion after Dryden's presentation, “turbulence can be considered from two different standpoints. The first is that of pure science, the second that of application of the laws of turbulent motion, for instance to problems concerning airplanes.” For the former he suggested focussing on “a simple and well definable problem” such as the case of a rotating circular cylinder in an unlimited fluid; for the latter he pointed to the role of vibrations as a source of turbulence. (A few years later Dryden would study “boundary layer flutter” and confirm the Tollmien-Schlichting theory). Prandtl remarked that the laws observed for different kinds of turbulence are not the same. Therefore, the study of a rotating cylinder would contribute little to the understanding of other cases, such as the flow along a straight wall (Dryden Reference Dryden, Hartog and Peters1938, 368).
After his return to Germany, Prandtl confided to a colleague that according to his opinion the symposium on turbulence was “not particularly successful”: “There have been gathered from all sides a whole lot of bricks and other raw materials, but it has not yet become apparent how the edifice should look like which can be built from it. Perhaps one has to prepare later a second symposium in which the construction plan can be clarified.” Footnote 12
Prandtl's misgivings after this symposium were aggravated by his alienation from the international community as a result of his political views. “I realized that you know nothing of what the criminal lunatic who rules your country has been doing,” Taylor recalled Prandtl's defense of Hitler's policy with regard to the Sudeten crisis, “and so you will not be able to understand the hatred of Germany which has been growing for some years in every nation which has a free press.”Footnote 13 Prandtl responded with even stronger expressions of his agreement with Nazi politics (Eckert Reference Eckert2017, chap. 7.11). Politics now added a further divide to the division of disciplines and institutions in which turbulence research was performed. With respect to its internationality, the interwar period ended even before the outbreak of the Second World War separated the international community of scientists and engineers into different camps.
Conclusion
Despite all divides: Turbulence had grown into a distinct research field during the interwar period. A number of specific research topics of Prandtl's institute during the war focussed on turbulence – both with an orientation on wartime applications and on more fundamental questions (Eckert Reference Eckert2017, chap. 8.7 and 8.8). After the war, Prandtl and his part-time collaborator Henry Görtler reviewed turbulence research in Germany during the war in reports solicited by the Field Information Agency, Technical (FIAT) of the US-Army (Prandtl Reference Prandtl and Betz1947; Görtler Reference Görtler and Walther1948). In the United States, Kármán's collaborators, Hans Wolfgang Liepmann and John Laufer, authored a 60-page NACA-report about their measurements on turbulent shear flow, which constituted “one part of a long-range research program on the development and nature of turbulent flow” at the GALCIT (Liepmann and Laufer Reference Liepmann and Laufer1947). NBS-researchers reviewed the hotwire technology for the investigation of turbulent boundary layers (Schubauer and Klebanoff Reference Schubauer and Klebanoff1946). At the first International Congress for Applied Mechanics after the war, held in September 1946 in Paris, the organizers arranged again a special “turbulence symposium,” like the symposium from 1938, but this time subdivided into several sessions. Dryden reported in Science how much interest this event arose among the participants (Dryden Reference Dryden1947). It is obvious that this and similar gatherings of turbulence researchers at the subsequent International Congresses for Applied Mechanics, now under the umbrella of the International Union of Theoretical and Applied Mechanics (IUTAM), continued the tradition of the pre-war mechanics congresses. The flourishing of turbulence research under this new roof was based on its prior growth in the inter-war period (Eckert Reference Eckert2012).
From an epistemological vantage point it is tempting to label turbulence research as just another engineering science, like highspeed aerodynamics or other specialties that emerged with the demands of aviation in heretofore unexplored applications (Anderson Reference Anderson, Galison and Roland2000; Vincenti Reference Vincenti1997 and Reference Vincenti, Galison and Roland2000; Vincenti and Bloor Reference Vincenti and Bloor2003). Walter G. Vincenti clearly distinguished the epistemology in these research fields from the production of knowledge in science (Vincenti Reference Vincenti1990). However, Vincenti's engineering epistemology with its “variation-selection model” for knowledge production cannot cope with those features of turbulence that were perceived as “the turbulence problem,” which involved non-engineers like Sommerfeld and Heisenberg as well as the “scientific engineers” Prandtl and Kármán. The more we extend the time frame, the less coherent turbulence appears as a research field. Its development in the twentieth century is reminiscent of the joke about the muddle-headed professor who had made great discoveries – but had forgotten what was the question. While Sommerfeld and his school regarded the turbulence problem as the challenge to determine the onset of turbulence in terms of hydrodynamic instability, later generations of turbulence researchers discerned the statistical theory of fully developed turbulence as the greater challenge. The surge of turbulence research after WW II exposed new riddles. When Hans Liepmann addressed the “turbulence problem” in the 1970s he added “whatever that means” (Liepmann Reference Liepmann1979, 221). At a symposium on “Fundamental Problems of Turbulence” in 2011 it became abundantly clear that the pattern of turbulence research had become ever more complex (Farge et al. Reference Farge, Moffatt and Schneider2014).
If turbulence acquired nevertheless a distinct identity as a challenging research field, what kind of entity did it represent? A subdiscipline of physics, like solid-state physics? Or a hybrid like biophysics or astrophysics? Or an entirely new discipline? None of these categorizations appear adequate. They ignore the multifaceted character of turbulence which attracted researchers beyond disciplinary boundaries, from mathematics to engineering. The role of interactions with technology cannot be overrated: turbulent pipe flow in hydraulics, turbulent skin friction in the design of surfaces from naval architecture to aeronautics, wind tunnel turbulence in model testing – to recall just the most prominent technological applications from the inter-war period. Furthermore, interactions with technology went both ways: turbulence was not only a research field with important consequences for all kinds of applications, but also driven by technology, such as when the availability of sophisticated electronics in the 1920s sparked the development of hotwire animometry for measuring turbulent fluctuations in wind tunnels.
Prandtl and Kármán epitomized this interaction of basic research with engineering like few others. As David Bloor has observed with regard to the trip-wire experiment from 1914, “Prandtl's engineering mind linked a novel theoretical idea to a novel technology of intervention” (Bloor Reference Bloor2011, 254). When Prandtl reflected many years later about his methodological approach in fluid mechanics he emphasized the role of visualization and ostensive understanding (Anschauung). He was striving for a thorough visual understanding before he approached a problem mathematically: “The equations come only later when I believe that I have grasped the matter; for one part they serve to obtain quantitative predictions which of course one cannot get by visualization alone; for the other part the equations are an appropriate means in order to prove my conclusions so that other people become convinced as well” (Prandtl Reference Prandtl1948, 89). Thus even in their quest for a more basic understanding of turbulence, scientific engineers like Prandtl regarded “the equations” more as a tool than as the goal of their research. In terms of disciplinary classification, technical or applied mechanics would be the closest labelling – at least in Germany in the inter-war period. The attribute “applied” became the constitutive element of this research field – both as a label for the umbrella under which its results were communicated (ZAMM, GAMM etc.) and as an expression about the role of engineering and technology in the quest for scientific results. Although it is too early to interpret the historical development of turbulence research from the perspective of one or another epistemological framework: it is safe to conclude that the notion “applied” will be essential in this epistemology, whatsoever the fundamental questions are from a “pure” scientific perspective.
