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12 - Philip G. Saffman

Published online by Cambridge University Press:  07 October 2011

By
D.I. Pullin  and
Daniel I. Meiron
Edited by
Peter A. Davidson ,
Yukio Kaneda ,
Keith Moffatt  and
Katepalli R. Sreenivasan
D.I. Pullin
Affiliation:
Graduate Aerospace Laboratories
Daniel I. Meiron
Affiliation:
Graduate Aerospace Laboratories
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
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Summary

Introduction

Philip G. Saffman was a leading theoretical fluid dynamicist of the second half of the twentieth century. He worked in many different sub-fields of fluid dynamics and, while his impact in other areas perhaps exceeded that in turbulence research, which is the topic of this article, his contributions to the theory of turbulence were significant and remain relevant today. He was also an incisive and, some might conclude, a somewhat harsh critic of progress or what he perceived as the lack thereof, in solving ‘the turbulence problem’. This extended to his own work; he stated in a preface to lectures on homogeneous turbulence (Saffman, 1968) that

the ideas … are new and hopefully important, but are speculative and quite possibly in serious error.

In this article, we will try to survey Saffman's thinking and contribution to turbulence research from the mid 1950s, when he began to mature as a scholar, until the late 1970s when he moved away from the study of turbulence to concentrate on the related but separate area, of the dynamics of isolated and interacting vortices. Although, for the most part, the evolution of his ideas and their application to turbulence in this period developed both thematically and chronologically together, where there are departures we will tend to focus on the former.

Type
Chapter
Information
A Voyage Through Turbulence , pp. 393 - 425
Publisher: Cambridge University Press
Print publication year: 2011

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References

Batchelor, G.K. 1951. Pressure fluctuations in isotropic turbulence. Proceedings of the Cambridge Philosophical Society, 47, 359.CrossRefGoogle Scholar
Batchelor, G.K. 1952. The effect of homogeneous turbulence on material lines and surfaces. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 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. Journal of Fluid Mechanics, 5(01), 113–133.CrossRefGoogle Scholar
Batchelor, G.K. 1969. Computation of the energy spectrum in homogeneous two-dimensional turbulence. Physics of Fluids (Supp. 2), 12, 233.Google Scholar
Batchelor, G.K. and Proudman, I. 1956. The large-scale structure of homogeneous turbulence. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 248(949), 369–405.CrossRefGoogle Scholar
Batchelor, G.K. and Townsend, A.A. 1956. Turbulent diffusion. In Surveys in Mechanics, G.K., Batchelor, ed., Cambridge University Press, 352–399.Google Scholar
Berkooz, G., Holmes, P. and Lumley, J.L. 1993. The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics, 25, 539–575.CrossRefGoogle Scholar
Bradshaw, P. 1977. Complex turbulent flows. In Theoretical and Applied Mechanics; Proceedings of the Fourteenth International Congress, Delft, Netherlands, August 30–September 4, 1976. (A78-13990 03–31) Amsterdam,North-Holland Publishing Co., 1977, 103–113.Google Scholar
Brown, G.L. and Roshko, A. 1974. Density effects and large structure in turbulent mixing layers. Journal of Fluid Mechanics, 64, 775–816.CrossRefGoogle Scholar
Cocke, W.J. 1969. Turbulent hydrodynamic line stretching. Consequences of isotropy. Physics of Fluids, 12, 2488.CrossRefGoogle Scholar
Cohen, S. 1999. Philip Saffman, a memoir. Caltech Archives, 1, 1–91.Google Scholar
Davidson, P.A. 2009. The role of angular momentum conservation in homogeneous turbulence. Journal of Fluid Mechanics, 32, 329–358.CrossRefGoogle Scholar
Etemadi, N. 1990. On curve and surface stretching in isotropic turbulent flow. Journal of Fluid Mechanics, 221, 685–692.CrossRefGoogle Scholar
Forster, D., Nelson, D.R. and Stephen, M.J. 1977. Large-distance and long-time properties of a randomly stirred fluid. Physical Review A, 16(2), 732–749.CrossRefGoogle Scholar
Govindaraju, S.P. and Saffman, P.G. 1971. Flow in a turbulent trailing vortex. Physics of Fluids, 14, 2074.CrossRefGoogle Scholar
Hoffmann, E.R. and Joubert, P.N. 1963. Turbulent line vortices. Journal of Fluid Mechanics, 16, 395–411.CrossRefGoogle Scholar
Hogge, H.D. and Meecham, W.C. 1978. The Wiener–Hermite expansion applied to decaying isotropic turbulence using a renormalized time-dependent base. Journal of Fluid Mechanics, 85, 325–347.CrossRefGoogle Scholar
Jiménez, J. 2003. Computing high-Reynolds-number turbulence: will simulations ever replace experiments?Journal of Turbulence, 4, 1–13.CrossRefGoogle Scholar
Kline, S.J., Reynolds, W.C., Schraub, F.A. and Runstadler, P.W. 1967. The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30, 741–773.CrossRefGoogle Scholar
Knight, D. 1975. Turbulence-model predictions for a flat plate boundary layer. AIAA Journal, 13, 945–947.CrossRefGoogle Scholar
Knight, D.D. and Saffman, P.G. 1978. Turbulence model predictions for flows with significant mean streamline curvature. In AIAA, Aerospace Sciences Meeting.
Kolmogorov, A.N. 1941. Dissipation of energy in locally isotropic turbulence. Izv. Akad. Nauk. SSR Seria fizichka, 32, 16–18.Google Scholar
Kolmogorov, A.N. 1942. Equations of turbulent motion in an incompressible liquid. Izv. Akad. Nauk. SSR Seria fizichka, VI, 56.Google Scholar
Kolmogorov, A.N. 1962a. Precisions sur la structure locale de la turbulence dans un fluide visqueux aux nombres de Reynolds élevés. In Mecanique de la Turbulence; Colloques Internationaux du Centre National de la Recherche Scientifique. CNRS, 447–458.
Kolmogorov, A.N. 1962b. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds numbers. Journal of Fluid Mechanics, 13, 82–85.CrossRefGoogle Scholar
Kraichnan, R.H. 1967. Inertial ranges in two-dimensional turbulence. Physics of Fluids, 10, 1417.CrossRefGoogle Scholar
Krogstad, P.A., and Davidson, P.A. 2010. Is grid turbulence Saffman turbulence?Journal of Fluid Mechanics, 642, 373–394.CrossRefGoogle Scholar
Kuznetsov, E.A., Naulin, V., Nielsen, A.H. and Rasmussen, J.J. 2007. Effects of sharp vorticity gradients in two-dimensional hydrodynamic turbulence. Physics of Fluids, 19, 105110.CrossRefGoogle Scholar
Landau, L., and Lifshitz, E. 1987. Fluid Mechanics. Butterworth-Heinemann.Google Scholar
Leonard, A. 1974a. Energy cascade in large-eddy simulations of turbulent fluid flows. Advance in Geophysics, 18A, 237–248.Google Scholar
Leonard, A. 1974b. Numerical studies of turbulence using vortex filaments. Bulletin of the Americal Physical Society, 19, 1163–1164.Google Scholar
Leslie, D.C. 1973. Developments in the Theory of Turbulence. Oxford University Press.Google Scholar
Liepmann, H.W. 1979. The rise and fall of ideas in turbulence. American Scientist, 67, 221–228.Google Scholar
Livescu, D., Ristorcelli, J.R., Gore, R.A., Dean, S.H., Cabot, W.H. and Cook, A.W. 2009. High-Reynolds number Rayleigh–Taylor turbulence. Journal of Turbulence, 10(13), 1–32.CrossRefGoogle Scholar
Loitsyanski, L.G. 1939. Some basic laws for isotropic turbulent flow. Trudy Tsentr. Aero.-Gidrodyn, 3, 33.Google Scholar
Lundgren, T.S. 1967. Distribution functions in the statistical theory of turbulence. Physics of Fluids, 10, 969.CrossRefGoogle Scholar
Lundgren, T.S. 1982. Strained spiral vortex model for turbulent fine structure. Physics of Fluids, 25, 2193.CrossRefGoogle Scholar
Meecham, W.C. and Siegel, A. 1964. Wiener–Hermite expansion in model turbulence at large Reynolds number. Physics of Fluids, 7, 1178.CrossRefGoogle Scholar
Micheli, P.L. 1968. Dispersion in a turbulent field. PhD Thesis, Stanford University. Mickelsen, W.R. 1960. Measurements of the effect of molecular diffusivity in turbulent diffusion. Journal of Fluid Mechanics, 7, 397–400.Google Scholar
Moffatt, H.K. 1970. Turbulent dynamo action at low magnetic Reynolds number. Journal of Fluid Mechanics, 41, 435–452.CrossRefGoogle Scholar
Moffatt, H.K. 2007. The birth and adolescence of MHD turbulence. In Magnetohydro-dynamics – Historical Evolution and Trends, S., Molokov, R., Moreau and H.K., Moffatt, eds., 213–222.Google Scholar
Monin, A.S. and Yaglom, A.M. 1971. Statistical Fluid Mechanics, vols 1&2. MIT Press.Google Scholar
Moore, D.W. and Saffman, P.G. 1973. Axial flow in laminar trailing vortices. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 333(1595), 491–508.CrossRefGoogle Scholar
Moore, D.W. and Saffman, P.G. 1975. The density of organized vortices in a turbulent mixing layer. Journal of Fluid Mechanics, 69, 465–473.CrossRefGoogle Scholar
Moser, R.D., and Rogers, M.M. 1993. The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. Journal of Fluid Mechanics, 247, 275–320.CrossRefGoogle Scholar
Ohkitani, K. 2002. Numerical study of comparison of vorticity and passive vectors in turbulence and inviscid flows. Physical Review E, 65(4), 046304.CrossRefGoogle ScholarPubMed
Orszag, S. and Patterson, G. 1972. The numerical simulation of 3-dimensional homogeneous isotropic turbulence. Phys. Rev. Letters, 76.Google Scholar
Orszag, S.A. 1970. Comments on turbulent hydrodynamic line stretching. Consequences of isotropy. Physics of Fluids, 13, 2203.CrossRefGoogle Scholar
Pope, S.B. 1975. A more general effective-viscosity hypothesis. Journal of Fluid Mechanics, 72, 331–340.CrossRefGoogle Scholar
Proudman, I. and Reid, W.H. 1954. On the decay of a normally distributed and homogeneous turbulent velocity field. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 247, 163–189.CrossRefGoogle Scholar
Ruelle, D. 1976. Statistical mechanics and dynamical systems. Chapter I of Statistical Mechanics and Dynamical Systems by David Ruelle and papers from the 1976 Duke Turbulence Conference, Duke University Mathematics Series III.Google Scholar
Saffman, P.G. 1960. On the effect of the molecular diffusivity in turbulent diffusion. Journal of Fluid Mechanics, 8, 273–283.CrossRefGoogle Scholar
Saffman, P.G. 1962. Some aspects of the effects of the molecular diffusivity in turbulent diffusion. Colloques Internationaux du Centre National de la Recherche Scientifique, 53.
Saffman, P.G. 1963. On the fine-scale structure of vector fields convected by a turbulent fluid. Journal of Fluid Mechanics, 16, 545–572.CrossRefGoogle Scholar
Saffman, P.G. 1967. The large-scale structure of homogeneous turbulence. Journal of Fluid Mechanics, 27(03), 581–593.CrossRefGoogle Scholar
Saffman, P.G. 1968. Lectures on homogeneous turbulence. Topics in Nonlinear Physics, 485–614.
Saffman, P.G. 1969. Application of Wiener–Hermite expansion to diffusion of a passive scalar in a homogeneous turbulent field. Physics of Fluids, 12, 1786–1789.CrossRefGoogle Scholar
Saffman, P.G. 1970a. A model for inhomogeneous turbulent flow. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 317, 417–433.CrossRefGoogle Scholar
Saffman, P.G. 1970b. Dependence on Reynolds number of high-order moments of velocity derivatives in issotropic turbulence. Physics of Fluids, 13, 2193.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
Saffman, P.G. 1973. Structure of turbulent line vortices. Physics of Fluids, 16, 1181.CrossRefGoogle Scholar
Saffman, P.G. 1974. Model equations for turbulent shear flow. Studies in Applied Mathematics, 53, 17–34.CrossRefGoogle Scholar
Saffman, P.G. 1976. Development of a complete model for the calculation of turbulent shear flows. Chapter II of Statistical mechanics and Dynamical Systems by David Ruelle and papers from the 1976 Duke Turbulence Conference, Duke University Mathematics Series III.Google Scholar
Saffman, P.G. 1977. Results of a two equation model for turbulent flows and development of a relaxation stress model for application to straining and rotating flows. In Turbulence in Internal Flows: Turbomachinery and Other Engineering Applications; Proceedings of the SQUID Workshop, Warrenton, VA., June 14, 15, 1976. (A78-34826 14–34) Washington, DC. Hemisphere Publishing Corp., 1977, 191–226; Discussion, 226–231.Google Scholar
Saffman, P.G. 1978. Problems and progress in the theory of turbulence. In Structure and Mechanisms of Turbulence II, 273–306.
Saffman, P.G. and Turner, J.S. 1956. On the collision of drops in turbulent clouds. Journal of Fluid Mechanics, 1, 16–30.CrossRefGoogle Scholar
Schlatter, P. and Örlü, R. 2010. Assessment of direct numerical simulation data of turbulent boundary layers. Journal of Fluid Mechanics, 659, 116–126.CrossRefGoogle Scholar
Schumann, U. 1977. Realizability of Reynolds-stress turbulence models. Physics of Fluids, 20, 721.CrossRefGoogle Scholar
Sreenivasan, K.R. 1984. On the scaling of the turbulent energy dissipation rate. Physics of Fluids, 5, 1048.CrossRefGoogle Scholar
Synge, J.L. and Lin, C.C. 1943. On a statistical model of isotropic turbulence. Trans. Roy. Soc. Canada, 37, 45–63.Google Scholar
Taylor, G.I. 1922. Diffusion by continuous movements. Proc. London Math. Soc, 2(20), 196–212.CrossRefGoogle Scholar
Taylor, G.I. 1935. Statistical theory of turbulence. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 151(873), 421–444.CrossRefGoogle Scholar
Townsend, A.A. 1951. On the fine-scale structure of turbulence. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 208, 534–542.CrossRefGoogle Scholar
Townsend, A.A. 1954. The diffusion behind a line source in homogeneous turbulence. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 224(1159), 487–512.CrossRefGoogle Scholar
Tsinober, A. and Galanti, B. 2003. Exploratory numerical experiments on the difference between genuine and ‘passive’ turbulence. Physics of Fluids, 15, 3514–3531.CrossRefGoogle Scholar
Wilcox, D.C. 1975. Turbulence-model transition predictions. AIAA Journal, 13, 241–243.CrossRefGoogle Scholar
Winant, C.D. and Browand, F.K. 1974. Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. Journal of Fluid Mechanics, 63(02), 237–255.CrossRefGoogle Scholar
Yaglom, A.M. 1994. A.N. Kolmogorov as a fluid mechanician and founder of a school in turbulence research. Annual Review of Fluid Mechanics, 26(1), 1–23.CrossRefGoogle Scholar

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