Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-11T17:32:42.939Z Has data issue: false hasContentIssue false

8 - George Batchelor: the post-war renaissance of research in turbulence

Published online by Cambridge University Press:  07 October 2011

By
H.K. Moffatt
Edited by
Peter A. Davidson ,
Yukio Kaneda ,
Keith Moffatt  and
Katepalli R. Sreenivasan
H.K. Moffatt
Affiliation:
University of Cambridge
Peter A. Davidson
Affiliation:
University of Cambridge
Yukio Kaneda
Affiliation:
Nagoya University, Japan
Keith Moffatt
Affiliation:
University of Cambridge
Katepalli R. Sreenivasan
Affiliation:
New York University
Get access

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.

Type
Chapter
Information
A Voyage Through Turbulence , pp. 276 - 304
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barenblatt, G.I. 2001. George Keith Batchelor (1920–2000) and David George Crighton (1942–2000): Applied Mathematicians. Notices Amer. Math. Soc. 48, 800–806.Google Scholar
Batchelor, G.K. 1946a. The theory of axisymmetric turbulence. Proc. Roy. Soc. A 186, 480–502.CrossRefGoogle Scholar
Batchelor, G.K. 1946b. Double velocity correlation function in turbulent motion. Nature 158, 883–884.CrossRefGoogle Scholar
Batchelor, G.K. 1947. Kolmogoroff's theory of locally isotropic turbulence. Proc. Cam. Phil. Soc. 43, 533–559.CrossRefGoogle Scholar
Batchelor, G.K. 1949a. The role of big eddies in homogeneous turbulence. Proc. Roy. Soc. A 195, 513–532.CrossRefGoogle Scholar
Batchelor, G.K. 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
Batchelor, G.K. 1950a. On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. Roy. Soc. A 201, 405–416.CrossRefGoogle Scholar
Batchelor, G.K. 1950b. The application of the similarity theory of turbulence to atmospheric diffusion. Quarterly Journal of the Royal Meteorological Society 76, 133–146.CrossRefGoogle Scholar
Batchelor, G.K. 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.
Batchelor, G.K. 1952a. Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Cam. Phil. Soc. 48, 345–362.CrossRefGoogle Scholar
Batchelor, G.K. 1952b. The effect of homogeneous turbulence on material lines and surfaces. Proc. Roy. Soc. A 213, 349–366.CrossRefGoogle Scholar
Batchelor, G.K. 1953. The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G.K. 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
Batchelor, G.K. 1964. Diffusion from sources in a turbulent boundary layer. Arch. Mech. Stosowanech 16, 661–670.Google Scholar
Batchelor, G.K. 1967. An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Batchelor, G.K. 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
Batchelor, G.K. 1980. Mass transfer from small particles suspended in turbulent fluid. J. Fluid Mech. 98, 609–623.CrossRefGoogle Scholar
Batchelor, G.K. 1992. Fifty years with fluid mechanics. Proc. 11th Australian Fluid Mechanics Conf., Dec. 1992, 1–8.
Batchelor, G.K. 1996. The Life and Legacy of G.I. Taylor, Cambridge University Press.Google Scholar
Batchelor, G.K. 1997. Research as a life style. Appl. Mech. Rev. 50, R11–R20.CrossRefGoogle Scholar
Batchelor, G.K. & Proudman, I. 1954. The effect of rapid distortion of a fluid in turbulent motion. Quart. Journ. Mech. and Applied Math. 7, 83–103.CrossRefGoogle Scholar
Batchelor, G.K. & Proudman, I. 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
Batchelor, G.K. & Townsend, A.A. 1947. Decay of vorticity in isotropic turbulence. Proc. Roy. Soc. A 190, 534–550.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 1948a. Decay of isotropic turbulence in the initial period. Proc. Roy. Soc. A 193, 539–558.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 1948b. Decay of turbulence in the final period. Proc. Roy. Soc. A 194, 527–543.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 1949. The nature of turbulent motion at large wave-numbers. Proc. Roy. Soc. A 199, 238–255.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 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
Batchelor, G.K., Binnie, A.M. & Phillips, O.M. 1955. The mean velocity of discrete particles in turbulent flow in a pipe. Proc. Phys. Soc. B 68, 1095–1104.CrossRefGoogle Scholar
Batchelor, G.K., Canuto, V.M. & Chasnov, J.R. 1992. Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349–378.CrossRefGoogle Scholar
Batchelor, G.K., Howells, I.D. & Townsend, A.A. 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
Corrsin, S. 1951. On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473.CrossRefGoogle Scholar
Cowling, T.G. 1957. Magnetohydrodynamics. Interscience Publishers Inc.Google Scholar
Eyink, G., Frisch, U., Moreau, R. & Sobolevskii, A. (eds) 2008. Euler equations: 250 years on. Physics D237.
Favre, A. (ed) 1962. Mécanique de la Turbulence. No. 108, Editions du CNRS.
Frisch, U. 1995. Turbulence, the Legacy of A.N. Kolmogorov. Cambridge University Press.Google Scholar
Grant, H.L., Stewart, R.W. & Moilliet, A. 1962. Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–268.CrossRefGoogle Scholar
Ishida, T., Davidson, P.A. & Kaneda, Y. 2006. On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475.CrossRefGoogle Scholar
Kolmogorov, A.N. 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
Kolmogorov, A.N. 1941b. Dissipation of energy under locally isotropic turbulence. C.R. Acad. Sci. URSS 32, 16–18.Google Scholar
Kolmogorov, A.N. 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
Kraichnan, R.H. 1959. The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.CrossRefGoogle Scholar
Kraichnan, R.H. 1967. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.CrossRefGoogle Scholar
Kulsrud, R.M. 1999. A critical review of galactic dynamos. Ann. Rev. Astron. Astrophys. 37, 37–64.CrossRefGoogle Scholar
Moffatt, H.K. 1970. Turbulent dynamo action at low magnetic Reynolds number. J. Fluid Mech. 41, 435–452.CrossRefGoogle Scholar
Moffatt, H.K. 2002. George Keith Batchelor, 8 March 1920–30 March 2000. Biog. Mems. Fell. R.Soc. Lond. 48, 25–41.CrossRefGoogle Scholar
Moffatt, H.K. 2010. George Batchelor: a personal tribute, ten years on. J. Fluid Mech. 663, 2–7.CrossRefGoogle Scholar
Moffatt, H.K. & Saffman, P.G. 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
Obukhov, A.M. 1949. Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk, SSSR, Geogr. i Geofiz. 13, 58–69.Google Scholar
Saffman, P.G. 1963. On the fine-scale structure of vector fields convected by a turbulent fluid. J. Fluid Mech. 16, 542–572.CrossRefGoogle Scholar
Saffman, P.G. 1967. The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.CrossRefGoogle Scholar
Saffman, P.G. 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
Sagaut, P. & Cambon, C. 2008. Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Schlüter, A. & Biermann, L. 1950. Interstellare Magnetfelder. Z. Naturforsch. 5a, 237–251.Google Scholar
Steenbeck, M., Krause, F. & Rädler, K.-H. 1966. Berechnung der mittleren LorentzFeldstärke für ein elektrisch leitendes Medium in turbulenter, durch CoriolisKräfte beeinfluster Bewegung. Z. Naturforsch. 21a, 369–376.Google Scholar
Taylor, G.I. 1921. Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212.Google Scholar
Taylor, G.I. 1935. Turbulence in a contracting stream. Z. angew. Math. Mech. 15, 91–96.CrossRefGoogle Scholar
Taylor, G.I. 1954. The dispersion of matter in turbulent flow through a pipe. Proc. Roy. Soc. A 223, 446–68.CrossRefGoogle Scholar
Taylor, G.I. & Batchelor, G.K. 1949. The effect of wire gauze on small disturbances in a uniform stream. Quart. J. Mech. Appl. Math. 2, 1–29.CrossRefGoogle Scholar
Taylor, G.I. & Green, A.E. 1937. Mechanism of the production of small eddies from large ones. Proc. Roy. Soc. A 158, 499–521.CrossRefGoogle Scholar
Townsend, A.A. 1951a. The passage of turbulence through wire gauzes. Quart. J. Mech. Appl. Math. 4, 308–329.CrossRefGoogle Scholar
Townsend, A.A. 1951b. On the fine-scale structure of turbulence. Proc. Roy. Soc. A 208, 534–542.CrossRefGoogle Scholar
Townsend, A.A. 1990. Early days of turbulence research in Cambridge. J. Fluid Mech. 212, 1–5.CrossRefGoogle Scholar
Zeldovich, Ya. B. 1957. The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. JETP 4, 460–462.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×