Skip to main content
SpringerLink
Log in

Turbulence: the chief outstanding difficulty of our subject

  • Originals
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

A review of interesting current topics in turbulence research is decorated with examples of popular fallacies about the behaviour of turbulence. Topics include the status of the Law of the Wall, especially in compressible flow; analogies between the effects of Reynolds number, pressure gradient, unsteadiness and roughness change; the status of Kolmogorov's universal equilibrium theory and local isotropy of the small eddies; turbulence modelling, with reference to universality, pressure-strain modelling and the dissipation equation; and chaos. Fallacies include the mixing-length concept; the effect of pressure gradient on Reynolds shear stress; the separability of time and space derivatives; models of the dissipation equation; and chaos.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akselvoll, K.; Moin, P. 1993: Large-eddy simulation of a backward-facing step flow. Engineering Turbulence Modelling and Experiments 2, (W. Rodi and F. Martelli, Eds.) Elsevier, pp 303–313.

  • Baldwin, B. S.; Barth, T. J. 1990: A one-equation turbulence transport model for high Reynolds number wall-bounded flows* NASA TM-102847: see also AIAA-91-0610, 1991.

  • Baldwin, B. S.; Lomax, H. 1978: Thin-layer approxiumation and algebraic model for separated turbulent flows. AIAA-78–257.

  • Birch, S. F.; Eggers, J. M. 1973: A critical review of the experimental data for developed free turbulent shear layers. NASA SP-321, pp 11–37.

  • Bradshaw, P. 1967: ‘Inactive’ motion and pressure fluctations in turbulent boundary layers. J Fluid Mech 30:241–258.

    Google Scholar 

  • Bradshaw, P. 1974: Possible origin of Prandtl's mixing length theory. Nature 249, 135–136.

    Google Scholar 

  • Bradshaw, P.; Mansour, N. N.; Piomelli, U. 1987: On local approximations of the pressure-strain term in turbulence models. Proceedings of the Summer Program 1987, NASA Ames-Stanford Center for Turbulence Research, pp 159—164.

  • Brown, G. L.; Roshko, A. 1974: On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.

    Google Scholar 

  • Coles, D. 1969: The young person's guide to the data. Computation of Turbulent Boundary Layers — 1968 AFOSR-IFP-Stanford Conference, vol II (D.E. Coles and E.A. Hirst, Eds), Thermosciences Division, Stanford University, pp 1–45.

  • Corrsin, S. 1973: Comment on ‘Transport equations in turbulence’. Phys. Fluids 16, 157–158.

    Google Scholar 

  • Diessler, R. G. 1989: On the Nature of Navier-Stokes Turbulence, NASA Tech. Memo. 109183.

  • Durbin, P. A. 1993: A Reynolds-stress model for near wall turbulence. J. Fluid Mech. 249, 465–498.

    Google Scholar 

  • Germano, M. 1992: Turbulence — the filtering approach. J. Fluid Mech. 238, 325–336.

    Google Scholar 

  • Gleick, J. 1988: Chaos: Making a New Science, Penguin Books, New York.

    Google Scholar 

  • Goldstein, S. 1972: The Navier-Stokes Equations and the Bulk Viscosity of Simple Gases. J. Math. and Phys. Sci. (University of Madras) 6, 225–261.

    Google Scholar 

  • Grant, H. L. 1958: The large eddies of turbulent motion. J. Fluid Mech. 4, 149–190.

    Google Scholar 

  • Hong, S. K.; Murthy, S. N. B. 1986: Pressure-strain correlations in curved wall boundary layers. AIAA J 24, 971–998.

    Google Scholar 

  • Huang, P. G.; Bradshaw, P.; Coakley, T. J. 1993: Turbulence models for compressible boundary layers. To appear in AIAA J, vol. 32.

  • Kays, W. M.; Crawford, M. E. 1993: Convective Heat and Mass Transfer, 3rd Ed, McGraw-Hill, New York.

    Google Scholar 

  • Keefe, L. 1990: Connecting coherent structures and strange attractors. Near-Wall Turbulence — 1988 Zaric Memorial Conference (S. J. Kline and N. H. Afgan, Eds.), Hemisphere, Washington, pp 63–80.

    Google Scholar 

  • Kuznetsov, V. R.; Praskovsky, A. A.; Sabelnikov, V. A. 1992: Finescale turbulence structure of intermittent shear flows. J. Fluid Mech. 243, 595–622.

    Google Scholar 

  • Lamb, H. 1916: Hydrodynamics. University Press, Cambridge.

  • Le, H.; Moin, P. 1992: Direct numerical simulation of turbulent flow over a backward-facing step. NASA Ames/Stanford Center for Turb. Research, Ann. Res. Briefs, pp 161–173.

  • Leslie, D. C. 1973: Developments in the Theory of Turbulence. Clarendon Press, Oxford.

    Google Scholar 

  • Papamoschou, D.; Roshko, A. 1989: The compressible turbulent shear layer — an experimental study. J. Fluid Mech. 197, 453–477.

    Google Scholar 

  • Robinson, S. K. 1991: The kinematics of turbulent boundary layer structure. PhD thesis, Stanford Univ., and NASA TM 103859: see also Ann. Rev. Fluid Mech. 23, 601–639.

  • Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.; Kreiss, H. O. 1991: The analysis and modeling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493.

    Google Scholar 

  • Selig, M.; Andreopoulos, J.; Muck, K.; Dussauge, J.; Smits, A. J. 1989: Turbulence structure in a shock wave/turbulent boundary layer interaction. AIAA J 27, 862–869.

    Google Scholar 

  • Simpson, R. L. 1967: The turbulent boundary layer on a porous plate: an experimental study of the fluid dynamics with injection and suction. PhD thesis and Rept. no HMT-2, Stanford University.

  • Spalart, P. R.; Allmaras, S. R. 1992: A one-equation turbulence model for aerodynamic flows. AIAA-92-0439.

  • Tardu, F. S.; Binder, G. 1993: Wall shear stress modulation in unsteady turbulent channel flow with high imposed frequencies. Phys. Fluids A5, 2028–2037.

    Google Scholar 

  • Townsend, A. A. 1956: The Structure of Turbulent Shear Flow. University Press, Cambridge.

    Google Scholar 

  • Townsend, A.A. 1961: Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.

    Google Scholar 

  • Wilcos, D. C. 1992: Dilatation-dissipation corrections for advanced turbulence models. AIAA J 30, 2639–2646.

    Google Scholar 

  • Wood, D. H. 1980: A reattaching, turbulent, thin shear layer. PhD thesis, Imperial College, London.

    Google Scholar 

  • Zeman, O. 1990; Dilatation dissipation — the concept and application in modeling compressible mixing layers. Phys Fluids A2, 178–188.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Dept., Stanford University, 94305, Stanford, CA, USA

    Peter Bradshaw

Authors
  1. Peter Bradshaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper was originally presented, as the Third Stewartson Memorial Lecture, at the Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, 1992. The present version includes some new material and omits some jokes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bradshaw, P. Turbulence: the chief outstanding difficulty of our subject. Experiments in Fluids 16, 203–216 (1994). https://doi.org/10.1007/BF00206540

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00206540

Keywords

Search

Navigation