Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Osborne Reynolds: a turbulent life
- 2 Prandtl and the Göttingen school
- 3 Theodore von Kármán
- 4 G.I. Taylor: the inspiration behind the Cambridge school
- 5 Lewis Fry Richardson
- 6 The Russian school
- 7 Stanley Corrsin
- 8 George Batchelor: the post-war renaissance of research in turbulence
- 9 A.A. Townsend
- 10 Robert H. Kraichnan
- 11 Satish Dhawan
- 12 Philip G. Saffman
- 13 Epilogue: a turbulence timeline
- References
8 - George Batchelor: the post-war renaissance of research in turbulence
Published online by Cambridge University Press: 07 October 2011
Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Osborne Reynolds: a turbulent life
- 2 Prandtl and the Göttingen school
- 3 Theodore von Kármán
- 4 G.I. Taylor: the inspiration behind the Cambridge school
- 5 Lewis Fry Richardson
- 6 The Russian school
- 7 Stanley Corrsin
- 8 George Batchelor: the post-war renaissance of research in turbulence
- 9 A.A. Townsend
- 10 Robert H. Kraichnan
- 11 Satish Dhawan
- 12 Philip G. Saffman
- 13 Epilogue: a turbulence timeline
- References
Summary
Introduction
George Batchelor (1920–2000), whose portrait (1984) by the artist Rupert Shephard is shown in Figure 8.1, was undoubtedly one of the great figures of fluid dynamics of the twentieth century. His contributions to two major areas of the subject, turbulence and low-Reynolds-number microhydrodynamics, were of seminal quality and have had a lasting impact. At the same time, he exerted great influence in his multiple roles as founder Editor of the Journal of Fluid Mechanics, co-Founder and first Chairman of EUROMECH, and Head of the Department of Applied Mathematics and Theoretical Physics (DAMTP) in Cambridge from its foundation in 1959 until his retirement in 1983.
I focus in this chapter on his contributions to the theory of turbulence, in which he was intensively involved over the period 1945 to 1960. His research monograph The Theory of Homogeneous Turbulence, published in 1953, appeared at a time when he was still optimistic that a complete solution to ‘the problem of turbulence’ might be found. During this period, he attracted an outstanding group of research students and post-docs, many from his native Australia, and Senior Visitors from all over the world, to work with him in Cambridge on turbulence. By 1960, however, it had become apparent to him that insurmountable mathematical difficulties in dealing adequately with the closure problem lay ahead.
Information
- Type
- Chapter
- Information
- A Voyage Through Turbulence , pp. 276 - 304Publisher: Cambridge University PressPrint publication year: 2011
References
2001. George Keith Batchelor (1920–2000) and David George Crighton (1942–2000): Applied Mathematicians. Notices Amer. Math. Soc. 48, 800–806.Google Scholar
1946b. Double velocity correlation function in turbulent motion. Nature 158, 883–884.CrossRefGoogle Scholar
1947. Kolmogoroff's theory of locally isotropic turbulence. Proc. Cam. Phil. Soc. 43, 533–559.CrossRefGoogle Scholar
1949a. The role of big eddies in homogeneous turbulence. Proc. Roy. Soc. A 195, 513–532.CrossRefGoogle Scholar
1949b. Diffusion in a field of homogeneous turbulence. I. Eulerian analysis. Australian Journal of Scientific Research Series A – Physical Sciences 2, 437–450.Google Scholar
1950a. On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. Roy. Soc. A 201, 405–416.CrossRefGoogle Scholar
1950b. The application of the similarity theory of turbulence to atmospheric diffusion. Quarterly Journal of the Royal Meteorological Society 76, 133–146.CrossRefGoogle Scholar
1951. Magnetic fields and turbulence in a fluid of high conductivity. In: Proceedings of the Symposium on the motion of gaseous masses of cosmical dimensions, Paris, August 16–19, 1949, “Problems of Cosmical Aerodynamics”, Central Air Documents Office, 149–155.
1952a. Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Cam. Phil. Soc. 48, 345–362.CrossRefGoogle Scholar
1952b. The effect of homogeneous turbulence on material lines and surfaces. Proc. Roy. Soc. A 213, 349–366.CrossRefGoogle Scholar
1959. Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
1964. Diffusion from sources in a turbulent boundary layer. Arch. Mech. Stosowanech 16, 661–670.Google Scholar
1969. Computation of the energy spectrum in homogeneous two-dimensional turbulence. High-speed computing in fluid dynamics. The Physics of Fluids Supplement 11, 233–239.Google Scholar
1980. Mass transfer from small particles suspended in turbulent fluid. J. Fluid Mech. 98, 609–623.CrossRefGoogle Scholar
1992. Fifty years with fluid mechanics. Proc. 11th Australian Fluid Mechanics Conf., Dec. 1992, 1–8.
& 1954. The effect of rapid distortion of a fluid in turbulent motion. Quart. Journ. Mech. and Applied Math. 7, 83–103.CrossRefGoogle Scholar
& 1956. The large-scale structure of homogeneous turbulence. Phil. Trans. Roy. Soc. London Series A. Mathematical and Physical Sciences, No. 949, 248, 369–405.CrossRefGoogle Scholar
& 1947. Decay of vorticity in isotropic turbulence. Proc. Roy. Soc. A 190, 534–550.CrossRefGoogle Scholar
& 1948a. Decay of isotropic turbulence in the initial period. Proc. Roy. Soc. A 193, 539–558.CrossRefGoogle Scholar
& 1948b. Decay of turbulence in the final period. Proc. Roy. Soc. A 194, 527–543.CrossRefGoogle Scholar
& 1949. The nature of turbulent motion at large wave-numbers. Proc. Roy. Soc. A 199, 238–255.CrossRefGoogle Scholar
& 1956. Turbulent diffusion. In: Surveys in Mechanics: a collection of surveys of the present position of research in some branches of mechanics: written in commemoration of the 70th birthday of Geoffrey Ingram Taylor.Cambridge University Press, 352–399.Google Scholar
, & 1955. The mean velocity of discrete particles in turbulent flow in a pipe. Proc. Phys. Soc. B 68, 1095–1104.CrossRefGoogle Scholar
, & 1992. Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349–378.CrossRefGoogle Scholar
, & 1959. Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2. The case of large conductivity. J. Fluid Mech. 5, 134–139.CrossRefGoogle Scholar
1951. On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473.CrossRefGoogle Scholar
, , & (eds) 2008. Euler equations: 250 years on. Physics D237.
(ed) 1962. Mécanique de la Turbulence. No. 108, Editions du CNRS.
, & 1962. Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–268.CrossRefGoogle Scholar
1941a. The local structure of turbulence in an incompressible fluid with very large Reynolds number. C.R. Acad. Sci. URSS 309, 301–5.Google Scholar
1941b. Dissipation of energy under locally isotropic turbulence. C.R. Acad. Sci. URSS 32, 16–18.Google Scholar
1962. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.CrossRefGoogle Scholar
1959. The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.CrossRefGoogle Scholar
1967. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.CrossRefGoogle Scholar
1999. A critical review of galactic dynamos. Ann. Rev. Astron. Astrophys. 37, 37–64.CrossRefGoogle Scholar
1970. Turbulent dynamo action at low magnetic Reynolds number. J. Fluid Mech. 41, 435–452.CrossRefGoogle Scholar
2002. George Keith Batchelor, 8 March 1920–30 March 2000. Biog. Mems. Fell. R.Soc. Lond. 48, 25–41.CrossRefGoogle Scholar
2010. George Batchelor: a personal tribute, ten years on. J. Fluid Mech. 663, 2–7.CrossRefGoogle Scholar
& 1964. Comment on “Growth of a weak magnetic field in a turbulent conducting fluid with large magnetic Prandtl number”. Phys. Fluids 7, 155.CrossRefGoogle Scholar
1949. Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk, SSSR, Geogr. i Geofiz. 13, 58–69.Google Scholar
1963. On the fine-scale structure of vector fields convected by a turbulent fluid. J. Fluid Mech. 16, 542–572.CrossRefGoogle Scholar
1967. The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.CrossRefGoogle Scholar
1971. On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Studies in Applied Mathematics 50, 377–383.CrossRefGoogle Scholar
, & 1966. Berechnung der mittleren LorentzFeldstärke für ein elektrisch leitendes Medium in turbulenter, durch CoriolisKräfte beeinfluster Bewegung. Z. Naturforsch. 21a, 369–376.Google Scholar
1954. The dispersion of matter in turbulent flow through a pipe. Proc. Roy. Soc. A 223, 446–68.CrossRefGoogle Scholar
& 1949. The effect of wire gauze on small disturbances in a uniform stream. Quart. J. Mech. Appl. Math. 2, 1–29.CrossRefGoogle Scholar
. & 1937. Mechanism of the production of small eddies from large ones. Proc. Roy. Soc. A 158, 499–521.CrossRefGoogle Scholar
1951a. The passage of turbulence through wire gauzes. Quart. J. Mech. Appl. Math. 4, 308–329.CrossRefGoogle Scholar
1951b. On the fine-scale structure of turbulence. Proc. Roy. Soc. A 208, 534–542.CrossRefGoogle Scholar
1990. Early days of turbulence research in Cambridge. J. Fluid Mech. 212, 1–5.CrossRefGoogle Scholar
1957. The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. JETP 4, 460–462.Google Scholar
Accessibility standard: Unknown
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
Accessibility compliance for the PDF of this chapter is currently unknown
and may be updated in the future.
- 2
- Cited by