A Journey Through Turbulence P. Davidson, Y. Kaneda, H.K. Moffatt, K.R. Sreenivasan Contents List of contributors page vii 1 Osborne Reynolds: a Turbulent Life 1 1.1 Introduction 1 1.2 Professorial Career 11 1.3 End piece 31 References 37 2 Prandtl and the Gottingen¨ School 40 2.1 Introduction 40 2.2 The Boundary Layer Concept, 1904–1914 42 2.3 A Working Program for a Theory of Turbulence 47 2.4 Skin friction and turbulence I: the 1/7th law 53 2.5 The mixing length approach 54 2.6 Skin friction and turbulence II: the logarithmic law and beyond 57 2.7 Fully Developed Turbulence I: 1932 to 1937 62 2.8 Fully Developed Turbulence II: 1938 68 2.9 Fully Developed Turbulence III: 1939 to 1945 75 2.10 Prandtl’s Two Manuscripts on Turbulence, 1944–1945 78 2.11 Conclusion 90 References 93 3 Theodore von Karm´ an´ 101 3.1 Introduction 101 3.2 The logarithmic law of the wall 103 3.3 Isotropic turbulence 109 3.4 Epilogue 123 References 124 iii iv Contents 4 G.I. Taylor: The Inspiration behind the Cambridge School 127 4.1 Opening remarks 127 4.2 Brief chronological account, focusing mostly on scientific career 131 4.3 Ideas originated in the period 1915–1921 134 4.4 The intervening period 141 4.5 Ideas explored in the period 1935–1940 143 4.6 A window into Taylor’s personality through his corre- spondence 153 4.7 Some reflections 168 References 178 5 Lewis Fry Richardson 187 5.1 Introduction 187 5.2 The 4/3 law 190 5.3 Richardson Cascade and Numerical Weather Prediction 199 5.4 Fractal Dimension 204 5.5 Conclusions 206 References 207 6 The Russian School 209 6.1 Physicist and pilot 209 6.2 Mathematician 212 6.3 Applied mathematicians 221 6.4 Theoretical physicist 229 6.5 Epilogue 233 References 234 7 Stanley Corrsin 238 7.1 Early Years 238 7.2 First Contributions at Caltech 239 7.3 Arrival in Baltimore 243 7.4 Structure of Scalar Fields in Isotropic Turbulence 245 7.5 Scalar Transport and Diffusion 248 7.6 Homogeneous Turbulence: Decay and Shear 255 7.7 The Geometry and Intermittency of Turbulence 259 7.8 Turbulence and Chemical Reactions 263 7.9 The Johns Hopkins Environment 266 7.10 Final Years 269 References 271 8 George Batchelor: The Post-War Renaissance of Research in Turbulence 276 Contents v 8.1 Introduction 276 8.2 Marseille (1961): a watershed for turbulence 278 8.3 Personal Background 280 8.4 Batchelor and the Kolmogorov theory of turbulence 281 8.5 Batchelor and the turbulent dynamo 285 8.6 The decay of homogeneous turbulence 287 8.7 Batchelor’s 1953 monograph, The Theory of Homoge- neous Turbulence 289 8.8 Rapid distortion theory 292 8.9 Turbulent diffusion 293 8.10 Two-dimensional turbulence 294 8.11 Later papers 296 8.12 George Batchelor as Editor and as Head of Department 297 8.13 International activity 299 8.14 Conclusion 301 References 301 9 A.A. Townsend 305 9.1 Early Years 305 9.2 Move to Cambridge 306 9.3 War Years 307 9.4 Return to Cambridge 308 9.5 Putting KO41 to the test 309 9.6 Shear Flows 313 9.7 The Townsend Hypotheses 314 9.8 Turbulent Shear Flows and Eddies 321 9.9 Meteorological and other flows 323 9.10 Concluding remarks 325 References 325 10 Robert H. Kraichnan 329 10.1 Introduction 329 10.2 Closures: realizability, Galilean invariance and the random coupling models; MHD turbulence 332 10.3 Statistical mechanics and two-dimensional turbulence 342 10.4 Intermittency 352 10.5 Miscellany and conclusions 359 References 364 11 Satish Dhawan 373 11.1 Introduction 373 11.2 The Caltech Years 374 vi Contents 11.3 At Bangalore 380 11.4 Dhawan’s approach to building engineering science 387 References 390 12 Philip G. Saffman 392 12.1 Introduction 392 12.2 The problem of turbulent diffusion 396 12.3 Contributions to the Theory of Homogeneous Turbulence 401 12.4 Saffman as critic 418 References 420 Contributors Brian Launder Department of Mechanical Engineering, University of Manch- ester, Manchester M, UK Derek Jackson Department of Mechanical Engineering, University of Manch- ester, Manchester M, UK Eberhard Bodenschatz, Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Fassberg 11, 37077 G¨ottingen, Germany Michael Eckert, Forschungsinstitut, Deutsches Museum, Museumsinsel 1, 80538 M¨unchen, Germany A. Leonard Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA, USA N. Peters RWTH, Aachen, Germany K. R. Sreenivasan, Courant Institute of Mathematical Sciences, and Depart- ment of Physics, New York University, NY 10012, USA Roberto Benzi Gregory Falkovich Israel Charles Meneveau Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA James J. Riley University of Washington, Seattle, WA, USA H.K. Moffatt Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, UK Ivan Marusic Department of Mechanical Engineering, University of Mel- bourne, Victoria, 3010, Australia T.B. Nickels Emmanuel College, Cambridge Gregory Eyink Department of Department of Applied Mathematics & Statis- tics, The Johns Hopkins University. Baltimore MD 21218, USA Uriel Frisch, UNS, CNRS, OCA, Lab. Cassiop´ee, B.P. 4229, 06304 Nice Cedex 4, France Roddam Narasimha IIT, Bangalore, India Dale I. Pullin Daniel I. Meiron vii 1 Osborne Reynolds: a Turbulent Life Brian Launder and Derek Jackson 1.1 Introduction 1.1.1 Scope Articles on Osborne Reynolds’ academic life and published works have ap- peared in a number of publications beginning with a remarkably perceptive anonymous obituary notice published in Nature within eight days of his death (on February 21st, 1912) and a more extensive account written by Horace Lamb, FRS and published by the Royal Society, Lamb (1913), about a year later. More recent reviews have been provided by Gibson (1946), a student of Reynolds and later an academic colleague, Allen (1970), who provided the opening article in a volume marking the passage of 100 years from Reynolds taking up his chair appointment at Manchester in 1868, and by Jackson (1995), in an issue of Proc. Roy. Soc. celebrating the centenary of the publication of Reynolds’ 1895 paper on what we now call the Reynolds decomposition of the Navier–Stokes equations, about which more will be said later in the present article. A significant portion of the present account, is therefore, devoted to Reynolds’ family and background and to hitherto unreported aspects of his character to enable his contributions as a scientist and engineer to be viewed in the context of his life as a whole. While inevitably, some of what is pre- sented here on his academic work will be known to those who have read the articles cited above, archive material held by the University of Manchester and The Royal Society and other material brought to light in the writers’ personal enquiries provide new perspectives on parts of his career. 1.1.2 Family Background Osborne Reynolds came from a well-established Suffolk family with strong clerical connections (Crisp, 1911), which between 1800 and 1880 owned some 1 2 Launder & Jackson 500 acres of land and much of the property around the small village of Debach located about 5 miles NNW of Woodbridge, (White, 1844). Starting in 1779, three consecutive rectors of the parish of Debach-with-Boulge came from the Reynolds family. The Rev. Robert Reynolds was instituted on September 6th of that year on his own petition. When he retired in September 1817 his son, the Rev. Osborne Shribb Reynolds became Rector. Then, on his death in De- cember 1848, his eldest son, the Rev. Osborne Reynolds, took over for a while. This last named, father of the main subject of this chapter, entered Cambridge University in 1832 as a fee-paying pensioner. After matriculating from Trinity College in 1833, he transferred to Queens’ College from whence he graduated in 1837 as 13th Wrangler, (Venn, 1954). At that point it seemed that he was destined to follow a clerical career like his father and grandfather before him for he was ordained a deacon in Ely Cathedral the following year and became a priest a year later. The Rev. Osborne Reynolds married Jane Bryer, nee´ Hickman, the 22-year- old widow of the late Rev. Thomas Bryer at Hampstead Church on June 25th 1839 (The Times, June 29th 1839). Their first child, Jane, was born in 1840 and, soon afterwards, they moved to Ireland where the Rev. Reynolds had obtained a position as principal of the First Belfast Collegiate College, in Donegall Place (Martins Belfast Directory 1842–43, p. 82). Their second child, Osborne, was born there on August 23rd 1842, (Crisp, 1911). It seems, however, that the Rev. Reynolds still saw a career in the church as his goal for in 1843 he returned to England with his family to take up an ap- pointment as curate at the parish church in Chesham, Buckinghamshire. How- ever, his tenure of this post proved to be short-lived. On February 6th 1844 his wife died as a result of complications following the birth, three weeks earlier, of their second son Edward (The Times, February 12th 1844), leaving the Rev. Reynolds with the responsibility of bringing up his three small children alone. That task, allied with the financial limitations of his post as curate at Chesham, provided the incentive for him to seek an alternative position. In October 1845 he was appointed headmaster of Dedham Grammar School in Essex. The Rev. Reynolds took up his post at the end of 1845 and held it for almost eight years (Jones, 1907).