The Turbulence Problem: A Persistent Riddle in Historical Perspective

By Michael Eckert

On the road toward a history of turbulence, this book focuses on what the actors in this research field have identified as the “turbulence problem”. Turbulent flow rose to prominence as one of the most persistent challenges in science. At different times and in different social and disciplinary settings, the nature of this problem has changed in response to changing research agendas.

This book does not seek to provide a comprehensive account, but instead an exemplary exposition on the environments in which problems become the subjects of research agendas, with particular emphasis on the first half of the 20th century.

• Language: English
• Publisher: Springer
• Release date: Oct 5, 2019
• ISBN: 9783030318635

Book preview

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Gerard Alberts

University of Amsterdam, Amsterdam, The Netherlands

Theodore Arabatzis

University of Athens, Athens, Greece

Bretislav Friedrich

Fritz Haber Institut der Max Planck Gesellschaft, Berlin, Germany

Ulf Hashagen

Deutsches Museum, Munich, Germany

Dieter Hoffmann

Max-Planck-Institute for the History of Science, Berlin, Germany

Simon Mitton

University of Cambridge, Cambridge, UK

David Pantalony

University of Ottawa, Ottawa, ON, Canada

Matteo Valleriani

Max-Planck-Institute for the History of Science, Berlin, Germany

More information about this series at http://​www.​springer.​com/​series/​10085

Michael Eckert

The Turbulence Problem

A Persistent Riddle in Historical Perspective

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Michael Eckert

Forschungsinstitut, Deutsches Museum, Munich, Germany

ISSN 2211-4564e-ISSN 2211-4572

SpringerBriefs in History of Science and Technology

ISBN 978-3-030-31862-8e-ISBN 978-3-030-31863-5

https://doi.org/10.1007/978-3-030-31863-5

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

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Preface

Turbulence belongs to the realm of fluid dynamics, a discipline founded on the solid pillars of classical mechanics. Its basic equations, the Navier–Stokes equations, have been established in the nineteenth century. Yet it is regarded as the last major unsolved problem of classical physics. The turbulence problem rose to prominence as one of the most persistent challenges of science. The eddies in the turbulent flow of a river or the smoke from a chimney elude a physical understanding from first principles.

In the course of the twentieth century, turbulence became a research field where high expectations met with recurrent frustration. This makes turbulence an ideal subject for the historian of science and technology. On the route towards a history of turbulence, this book is focused on what the actors in this research field perceived as the turbulence problem. At different times and in different social and disciplinary environments, the nature of this problem changed in response to changing research agendas.

When the participants in this quest review their research field, they focus on the progress made for solving the riddles of turbulence. In contrast to participants’ reviews, my emphasis is rather on the broader context in which the turbulence problem(s) became enunciated. I am aiming for historical authenticity by quoting as far as possible from contemporary sources (letters, reports, papers). If the original quote was in German, I translated it in English (indicated by Translation ME in the footnote). My narrative is descriptive and proceeds in chronological order from around 1900 to the last decade of the twentieth century, so that one or another variant of the turbulence problem will be revisited in subsequent chapters in different circumstances. I do not aim at a comprehensive account but rather at an exemplary exposition of the environments in which problems become items of research agendas. From this perspective, the turbulence problem also provides more general lessons for the history and epistemology of science and technology in the twentieth century.

Michael Eckert

Munich, Germany

August 2019

Abbreviations

AIP

American Institute of Physics, College Park, MD

APS

American Physical Society

ASWB

Arnold Sommerfeld. Wissenschaftlicher Briefwechsel. Band I: 1892–1918; Band II: 1919–1951. Herausgegeben von Michael Eckert und Karl Märker. München, Berlin, Diepholz: Deutsches Museum und GNT-Verlag, 2000 und 2004

DFD

Division of Fluid Dynamics of the American Physical Society

DFDA

Division of Fluid Dynamics of the American Physical Society, Archives, Lehigh University, Bethlehem, Pennsylvania

DLR

Deutsches Zentrum für Luft- und Raumfahrt

DMA

Deutsches Museum, Archiv, München

GAMM

Gesellschaft für Angewandte Mathematik und Mechanik

GOAR

Historical Archive of the DLR, Göttingen

IAS

Institute of the Aeronautical Sciences, New York

IAU

International Astronomical Union

IUGG

International Union of Geodesy and Geophysics

IUTAM

International Union of Theoretical and Applied Mechanics

NACA

National Advisory Committee for Aeronautics, Washington, D.C.

NPL

National Physical Laboratory, Teddington

RANH

Rijksarchief in Noord-Holland, Haarlem

SUB

Niedersächsische Staats- und Universitätsbibliothek, Göttingen

TKC

Theodore von Kármán Collection, California Institute of Technology, Pasadena

ZAMM

Zeitschrift für Angewandte Mathematik und Mechanik

ZWB

Zentrale für wissenschaftliches Berichtswesen der Luftfahrtforschung des Generalluftzeugmeisters

Contents

1 Hydrodynamics Versus Hydraulics 1

1.​1 When and How Turbulence Became a Problem 1

1.​2 Felix Klein’s Efforts to Bridge the Gulf Between Hydraulics and Hydrodynamics 3

1.​3 The Turbulence Problem in the Early Sommerfeld School 7

1.​4 Hydraulics and Turbulence 11

1.​5 Turbulence in the Wake of Spheres and Struts 15

2 The Turbulence Problem in the 1920s 17

2.1 The Turbulence Problem in ZAMM 17

2.​2 A New International Forum for Applied Mechanics 19

2.​3 The Great Problem of Developed Turbulence 21

2.​4 Tollmien’s Solution of the Stability Problem 22

2.​5 The Quest for a Universal Law of Turbulence 24

3 The Rise of Statistical Theories of Turbulence 27

3.​1 Atmospheric Turbulence 28

3.​2 Wind Tunnel Turbulence 29

3.​3 Taylor’s and Kármán’s Statistical Theories 31

3.​4 A Symposium on Turbulence 33

3.​5 Burgulence 35

4 Turbulence in WW II 39

4.​1 Kolmogorov’s Statistical Theory 40

4.​2 Laminar Wings 41

4.​3 Turbulence Problems in Miscellaneous War Applications 45

4.​4 Fundamental Wartime Research on Turbulence 47

5 Expectations and Hopes:​ 1945–1961 49

5.​1 A Remarkable Series of Coincidences 49

5.​2 The Turbulence Problem Ca.​ 1950 52

5.​3 Turbulence as a Challenge for American Physics 54

5.​4 The First Textbooks on Turbulence 57

5.​5 Marseille 1961 58

6 Computational Approaches 61

6.​1 John von Neumann and the Electronic Computer Project 62

6.​2 Early Numerical Solutions of the Stability Problem 63

6.​3 The Origins of Large-Eddy Simulation 66

6.​4 The Closure Problem 70

6.​5 Direct Numerical Simulation (DNS) 72

7 Chaos and Turbulence 75

7.​1 Strange Attractors 75

7.​2 Precision Experiments 78

7.​3 Fractals 80

7.​4 Coherent Structures 82

7.​5 Whither Turbulence 83

8 Turbulence as a Challenge for the Historian 87

References 91

Index 105

List of Figures

Fig. 1.1 Ludwig Prandtl, here in 1904 in front of a water tank built for studying the formation of vortices, made Gӧttingen a center for research on turbulence6

Fig. 1.2 Blasius’s diagram for the friction coefficient of laminar and turbulent pipe flow as a function of the Reynolds number (Blasius 1913, Abb. 13)14

Fig. 1.3 Transition to turbulence in the boundary layer of spheres results in a drop of the coeffient of friction $$ \psi $$ (displayed as a function of the Reynolds number). The measurements from Eiffel’s wind tunnel (dashed curves) indicate that the transition to turbulence occurred at a lower Reynolds number than in Prandtl’s wind tunnel (solid curves). Prandtl explained this by a higher degree of turbulence in Eiffel’s wind tunnel (Prandtl 1914, Fig. 1) (Courtesy University of Gӧttingen) 16

Fig. 2.1 Tollmien’s indifference diagram displays the demarcation between stable and unstable states of flow (Tollmien 1929, Abb. 4) (Courtesy University of Gӧttingen)23

Fig. 5.1 In May 1945 Hugh Dryden (left), Theodore von Kármán (with cigar) and others visited German aeronautic research facilities. At this opportunity they also learned about Prandtl’s recent efforts concerning the turbulence problem50

Fig. 6.1 John von Neumann (right) next to J. Robert Oppenheimer, director of the Princeton Institute for Advanced Study, in October 1952 at the dedication of the IAS computer65

Fig. 6.2 Schumann’s computation of turbulent velocities at one moment in an annular space. Arrows represent the velocity components in a plane perpendicular to the axis, contour lines the axial velocities (Schumann 1973, Fig. 17)69

Fig. 7.1 The Lorenz system:

$$ \frac{dx}{dt}=-\sigma x +\sigma y, \quad \frac{dy}{dt}=-xy+rx-y, \quad \frac{dz}{dt}=xy-bz $$

, as computed by Oscar Lanford and shown by David Ruelle in The Mathematical Intelligencer . The computation used the parameters $$ \sigma = 10 $$ , $$ r = 28 $$ , $$ b = 8/3 $$ and started at

$$ \{x=0, y=0, z=0\} $$

for $$ t=0 $$ . The vector

$$ \{x(t), y(t), z(t)\} $$

makes loops to the right and left in an irregular manner (Ruelle 1980, Fig. 3) 77

Fig. 7.2 A shadowgraph reveals coherent structures in the turbulent mixing layer of confluent jets of nitrogen and helium (Roshko 1991, Fig. 3)82

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

M. EckertThe Turbulence ProblemSpringerBriefs in History of Science and Technologyhttps://doi.org/10.1007/978-3-030-31863-5_1

1. Hydrodynamics Versus Hydraulics

Michael Eckert¹  

(1)

Forschungsinstitut, Deutsches Museum, Munich, Germany

Michael Eckert

Email: [e-mail]

Abstract

In the beginning of the 20th century the study of fluid motion fell into one of two classes: either the observed flow could be described in terms of hydrodynamics, or it eluded theory and belonged to the realm of hydraulic engineering, like pipe- or channel flow. The discrepant results of hydrodynamics versus hydraulics illustrated the gulf between theory and practice—and turbulence was regarded as the culprit. The rise of aeronautics added further challenges. Wind tunnel investigations hinted at turbulence effects that eluded theoretical analysis.

Research on turbulence has no clear-cut beginning. The history of quantum mechanics, by comparison, may be confined to the time span between Max Planck’s formula for black-body radiation in 1900 and the mid 1920s when Werner Heisenberg, Erwin Schrödinger and others established matrix- and wave mechanics. The history of turbulence has no such landmarks.

1.1 When and How Turbulence Became a Problem

Turbulent flow must have been observed since antiquity. It was surely perceived as strikingly different from the smooth flow regime later called laminar. The earliest observations of turbulence that left a trace in historic records are due to Leonardo da Vinci whose sketches of eddying water flow are frequently used in reviews on turbulence.¹ With the rise of rational fluid mechanics (Truesdell 1954) in the 18th century flow phenomena became subject of mathematical analysis. Johann and Daniel Bernoulli, Leonhard Euler, Jean-Baptiste le Rond d’Alembert and other pioneers of ideal flow theory must have been aware that there was a fundamental mismatch between theory and experiment which nearly always concerned eddying flow. Euler’s equation for ideal flow was extended in the first half of the 19th century to the Navier-Stokes equation by taking into account fluid friction—but that did not immediately foreground turbulence as a particular problem of hydrodynamic theory.

But hydraulic engineers concerned with the design of channels and water pipes had made turbulent flow already earlier a subject of experimental and theoretical studies, by . The history of turbulent flow formulae for the discharge of water in pipes and channels starts in the 18th century with Antoine Chézy, Albert Brahms and others. Thus a tradition of hydraulic flow studies was launched that resulted in well-established laws of turbulent flow—long before theory was up to derive them from the Navier-Stokes equation.² The first researcher who discerned the transition to turbulence as the culprit for discrepant flow laws was Gotthilf Hagen, an hydraulic engineer famous for his investigations published in 1839 of laminar pipe flow (Hagen-Poiseuille law). Fifteen years later Hagen reported about observations of two kinds of motions—similar to those for which Osborne Reynolds entered the hall of fame in turbulence more than three decades later (see below). Hagen visualized the transition to turbulence with sawdust added to a flow of water in a glass tube. I observed that for small pressures the sawdust propagated only in the direction of the tube, whereas for strong pressures it shot from one side to another and often assumed a vortical motion.³

From a theorist’s vantage point an early expression of what would later be called the turbulence problem is due to Adhémar Barré de Saint-Venant. The problem to establish in each case the differential equations for the motion and to integrate them has still its often great difficulty, he concluded in 1872 a study On the hydrodynamics of streams of water in which he reviewed recent efforts, among others, of his pupil Joseph Boussinesq. In contrast to the older theories of Navier and others Boussinesq’s approach was based on recent experiments by hydraulic engineers. From this respect, Saint-Venant concluded, the problem represents no longer this hopeless enigma which the distinguished minds have attacked in vain.⁴

When Osborne Reynolds published in 1883 his momentous study in which he established the concept of what later was named Reynolds number, turbulence had long been investigated and perceived as a riddle—even though in vague terms only. Reynolds introduced his treatise with the remark that the results of his investigation have both a practical and a philosophical aspect. The former concerned the law for the resistance in pipe flow, the latter the transition from laminar to turbulent flow, or, to speak with Reynolds, "a definite verification of two principles, which are—that the general character of the motion of fluids in contact with solid surfaces depends on the relation between a physical constant of the fluid and the product of the linear dimensions of the space occupied by the fluid and the velocity. He established the criterion which discriminates the direct from the sinuous flow, to use his own terms for the distinction between laminar and turbulent flow—but without the rhethoric of great enigma or riddle (Reynolds 1883) . Nor did George Gabriel Stokes and Lord Rayleigh, who acted as referees for the Royal Society, praise the paper as a major contribution in the quest for a theory of turbulence. Rayleigh’s verdict comprised 70 words and merely acknowledged that the results are important, and that the paper should be published in the Phil. Trans. With regard to the theoretical implication of Reynolds’  experimental findings he concluded that the Author refers to