Hostname: page-component-5cf477f64f-bmd9x Total loading time: 0 Render date: 2025-04-07T14:59:50.108Z Has data issue: false hasContentIssue false
  • English
  • Français

The understanding and prediction of turbulent flow

Published online by Cambridge University Press:  04 July 2016

P. Bradshaw
P. Bradshaw*
Affiliation:
Department of Aeronautics, Imperial College of Science and Technology, London
Get access Rights & Permissions [Opens in a new window]

Extract

It was easy for me to choose a subject for this lecture. First, turbulence is an important part of engineering fluid dynamics which has not so far been treated in the Reynolds-Prandtl lectures; secondly, it is the most obvious link between the careers of our two heroes; and thirdly it is the only scientific subject on which I am even remotely qualified to lecture before such a distinguished audience. The first and second propositions are sufficiently demonstrated by the annual consumption of something of the order of 1010kg of kerosene to overcome the effects of Reynolds’ stresses in Prandtl’s boundary layers. Have any two human beings ever had such a spectacular memorial? (Yes, Lanchester and Prandtl, to whose induced drag we sacrifice another 1010kg of fuel each year.)

Type
Research Article
Information
The Aeronautical Journal , Volume 76 , Issue 739 , July 1972 , pp. 403 - 418
Copyright
Copyright © Royal Aeronautical Society 1972 

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

1. Deardorff, J. W. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. Journal of Fluid Mechanics, Vol 41, p. 453, 1970. (This volume is devoted entirely to papers on turbulence and is a useful guide to current basic research.)Google Scholar
2. Donaldson, C. duP. Calculation of turbulent shear flows for atmospheric and vortex motions. AIAA Journal, Vol 10, p. 4, 1972.Google Scholar
3. Elliott, J. A. Microscale pressure fluctuations measured within the lower atmospheric boundary layer. Ph.D. Thesis, University of British Columbia, 1970.Google Scholar
4. Thompson, B. G. J. A critical review of existing methods of calculating the turbulent boundary layer. ARC R and M 3447, 1964.Google Scholar
5. Bradshaw, P. Variations on a theme of Prandtl. AGARD Conference Proceedings No. 93, 1971.Google Scholar
6. Morkovin, M. V. Effects of compressibility on turbulent flows. The Mechanics of Turbulence, Editor: Favre, A.. Gordon and Breach, 1964.Google Scholar
7. Rotta, J. C. Turbulent boundary layers in incompressible flow. Progress in Aeronautical Sciences, Vol 2, p. 5, 1962.Google Scholar
8. Bradshaw, P. Turbulent boundary layers. The Aeronautical Journal of the Royal Aeronautical Society, Vol 72, p. 689, 1968.Google Scholar
9. Reynolds, W. C. Computation of turbulent flows—State-of-the-art, 1970. Thermosciences Division, Stanford University, Report MD-27, 1970.Google Scholar
10. Bradshaw, P. An Introduction to Turbulence and its Measurement. Pergamon, 1971.Google Scholar
11. Townsend, A. A. The Structure of Turbulent Shear Flow, Cambridge, 1956.Google Scholar
12. Gupta, A. K., Laufer, J. and Kaplan, R. E. Spatial structure in the viscous sub-layer. Journal of Fluid Mechanics, Vol 50, p. 493, 1971.Google Scholar
13. Townsend, A. A. Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, Vol 11, p. 97, 1961.Google Scholar
14. Bradshaw, P. Special topics in turbulent flow. Lecture Series 10, von Karman Institute, 1969.Google Scholar
15. Kim, H. T., Kline, S. J. and Reynolds, W. C. The production of turbulence near a smooth wall in a turbulent boundary layer. Journal of Fluid Mechanics, Vol 50, p. 133, 1971.Google Scholar
16. Wallace, J. M., Eckelmann, H. and Brodkey, R. S. The wall region in turbulent shear flow. Max-Planck-Institut für Stromungsforschung Ber., 119, 1971.Google Scholar
17. Narahari Rao, K., Narasimha, R. and Badri Narayanan, . A. The “bursting” phenomenon in a turbulent bound ary layer. Journal of Fluid Mechanics, Vol 48, p. 339, 1971.Google Scholar
18. Grant, H. L. The large eddies of turbulent motion. Journal of Fluid Mechanics, Vol 4, p. 149, 1958.Google Scholar
19. Kovasznay, L. S. G., Kibens, V. and Blackwelder, R. F. Large-scale motion in the intermittent region of a boundary layer. Journal of Fluid Mechanics, Vol 41, p. 283, 1970.Google Scholar
20. Wyngaard, J. C. and Pao, Y. H. Some measurements of the fine structure of large Reynolds number turbulence. Proceedings, Symposium on Statistical Models and Turbulence, Springer-Verlag, 1971.Google Scholar
21. Mollo-Christensen, E. Physics of turbulent flow. AIAA Journal, Vol 9, p. 1217, 1971.Google Scholar
22. Hall, M. G. A model for the study of boundary-layer instability. RAE Tech Memo Aero 1118, 1969.Google Scholar
23. Donaldson, C. duP. A computer study of an analytical model of boundary layer transition. AIAA Paper No 68- 38, 1968.Google Scholar
24. Robertson, J. M. and Holt, C. F. Stream turbulence effects on the turbulent boundary layer. Proc ASCE, J Hydraulics Divn, 1972 (to be published).Google Scholar
25. Charnay, G., Comte-Bellot, G. and Mathieu, J. Development of a turbulent boundary layer on a flat plate in an external turbulent flow. AGARD Conference Proceedings No 93, 1971.Google Scholar
26. Coles, D. The turbulent boundary layer in a compressible fluid. Rand Corp Report R-403-PR, 1962 and ARC 24478, 1963.Google Scholar
27. Jones, W. P. and Launder, B. E. The prediction of laminarization with a two-equation model of turbulence. International Journal of Heat and Mass Transfer, Vol 15, p. 301, 1972.Google Scholar
28. Lawn, C. J. and Elliott, C. J. Fully-developed flow through concentric annuli. Central Electricity Generating Board Report RD/B/N1878, 1971.Google Scholar
29. Favre, A. Review on space-time correlation in turbulent fluids. Journal of Applied Mechanics, Vol 32E, p. 241, 1965. (Bibliography of Marseille work up to this date.)Google Scholar
30. Kline, S. J., Morkovin, M. V., Sovran, G. and Cock-Rell, D. J. (Editors). Proceedings, computation of turbulent boundary layers—1968 AFOSR-IFP-Stanford conference, Vol 1. Thermosciences Division, Stanford Univ., 1969.Google Scholar
31. Riegels, F. W. (Editor). Ludwig Prandtl Gesammelte Abhandlungen. Springer,1961.Google Scholar
32. Taylor, G. I. Some early ideas about turbulence. Journal of Fluid Mechanics, Vol 41, p. 3, 1970.Google Scholar
33. Kacker, S. C. and Whitelaw, J. H. The turbulence characteristics of two-dimensional wall-jet and wall-wake flows. Journal of Applied Mechanics, Vol 38E, p. 239, 1971.Google Scholar
34. Glushko, G. S. Turbulent boundary layer on a flat plate in an incompressible fluid. NASA TT F-10080. (Trans lation from Izw. Akad. Nauk, USSR, 1965.)Google Scholar
35. Spalding, D. B. Heat transfer from separated flow. Journal of Fluid Mechanics, Vol 27, p. 97, 1967.Google Scholar
36. Beckwith, I. E. and Bushnell, D. M. Detailed description and results of a method for computing mean and fluctuating quantities in turbulent boundary layers. NASA TN D-4815, 1968.Google Scholar
37. Harlow, F. H. and Nakayama, P. I. Turbulent transport equations. Physics of Fluids, Vol 10, p. 2323, 1967.Google Scholar
38. Rodi, W. and Spalding, D. B. A two-parameter model of turbulence and its application to free jets. Wärme und Stoffübertragung, Vol 3, p. 85, 1970.Google Scholar
39. Ng, K. H. and Spalding, D. B. Turbulence model for boundary layer near walls. Physics of Fluids, Vol 15, p. 20, 1972.Google Scholar
40. Saffman, P. G. A model for inhomogeneous turbulent flow. Proceedings of the Royal Society, Series A, Vol 317, p. 417, 1970.Google Scholar
41. Head, M. R. Entrainment in the turbulent boundary layer. ARC R & M 3152, 1958.Google Scholar
42. Head, M. R. and Patel, V. C. Improved entrainment method for calculating turbulent boundary layer development. ARC R & M 3643, 1968.Google Scholar
43. Bradshaw, P. Use of a refined boundary-layer calculation method to calibrate a simple one. Imperial College Aero Report 71-23, 1971.Google Scholar
44. Bradshaw, P. and Ferriss, D. H. Applications of a general method of calculating turbulent shear layers. Journal of Basic Engineering, Vol 94D, 1972. (ASME Paper No 71-WA/FE-8, 1971.)Google Scholar
45. Rotta, J. C. Statistische theorie nichthomogener turbulenz. Zeitschrift für Physik, Vol 129, p. 547 and Vol 131, p. 51, 1951.Google Scholar
46. Daly, B. J. and Harlow, F. H. Transport equations in turbulence. Physics of Fluids, Vol 13, p. 2634, 1970.Google Scholar
47. Rodi, W. On the equation governing the rate of turbulent energy dissipation. Imperial College Mech Engg Report TM/TN/A/14, 1971.Google Scholar
48. Hanjalic, K. and Launder, B. E. A Reynolds-stress model of turbulence and its application to thin shear flows. Journal of Fluid Mechanics, Vol 52, p. 609, 1972.Google Scholar
49. Donaldson, C. duP. and Rosenbaum, H. Calculation of turbulent shear flows through closure of the Reynolds equations by invariant modelling. ARAP Inc Report 127, 1968.Google Scholar
50. Mellor, G. L. and Herring, H. J. A study of turbulent boundary layer model. Part II, Mean turbulent field closure. Sandia Corp Report SC-CR-70-6125B, 1971.Google Scholar
51. Champagne, F. H., Harris, V. G. and Corrsin, S. Experiments on nearly homogeneous turbulent shear flow. Journal of Fluid Mechanics, Vol 41, p. 81, 1970.Google Scholar
52. Bradshaw, P. Calculation of three-dimensional turbulent boundary layers. Journal of Fluid Mechanics, Vol 46, p. 417, 1971.Google Scholar
53. Rotta, J. C Recent attempts to develop a generally applicable calculation method for turbulent shearflow layers. AGARD Conference Proceedings No 93, 1971.Google Scholar
54. Shamroth, S. J. and Elrod, H. G. The development of the Reynolds stress in a turbulent shear flow. Journal of Basic Engineering, Vol 92D, p. 836, 1970.Google Scholar
55. Lundgren, T. S. Model eauation for non-homogeneous turbulence. Physics of Fluids, Vol 12, p. 485, 1969.Google Scholar
56. Smith, A. M. O. A decade of boundary layer research. Applied Mechanics Reviews, Vol 23, p. 1, 1970.Google Scholar
57. Rotta, J. C. Turbulente Strömungen. Teubner, 1972.Google Scholar