Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-13T22:40:27.221Z Has data issue: false hasContentIssue false
  • English
  • Français

XVIII.—A Theory to Predict the Transport and Relaxation Properties of a Turbulent Fluid*

Published online by Cambridge University Press:  14 February 2012

J. R. Tyldesley
J. R. Tyldesley
Affiliation:
Department of Mechanical Engineering, University of Glasgow.
Get access Rights & Permissions [Opens in a new window]

Synopsis

A new approach to the analysis of transport processes in a turbulent fluid is presented In this approach a model is used to represent the detailed fluid behaviour and it is shown that the model has similarities with a Fourier integral representation of the flow field. The model assumes that the turbulent motions can be represented by fluid entities of random size, shape and velocity, and that the large-scale transport processes are the consequences of the creation, decay and mutual interaction of the individual entities. The effects of this are analysed and it is shown how the diffusivities for vector and scalar quantities can be determined in terms of properties of the turbulence. The theory is applied in both bounded and free turbulent flows and it is shown that the predicted diffusivity ratios compare favourably with experimental data. Relaxation phenomena are also investigated and the memory function for stress and thermal relaxation is determined. It is concluded that the model provides a most useful framework for the analysis of turbulence phenomena and that its diverse and accurate predictions make it a powerful research tool.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 68 , Issue 4 , 1970 , pp. 271 - 297
Copyright
Copyright © Royal Society of Edinburgh 1970

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

References to Literature

Batchelor, G. K., 1953. The theory of homogeneous turbulence. Cambridge University Press.Google Scholar
Clauser, F. H., 1956. “The turbulent boundary layer”, Adv. Appi. Math., 4, 1.Google Scholar
Crow, S. C. 1968. “Viscoelastic properties of fine-grained incompressible turbulence” J. Fluid Mech., 33, 1.CrossRefGoogle Scholar
Edwards, S. F., 1964. “The statistical dynamics of homogeneous turbulence”, J. Fluid Mech., 18, 239.CrossRefGoogle Scholar
Glushko, G. S., 1965. “Turbulent boundary layer on a flat plate in an incompressible fluid”, Izv. Akad. Nauk. SSSR (Mekh. Mashinost.), 4, 13.Google Scholar
Grant, H. L., 1958. “The large eddies of turbulent motion”, J. Fluid Mech., 4, 149.CrossRefGoogle Scholar
Heisenberg, W., 1948. “On the theory of statistical and isotropie turbulence”, Proc. Roy. Soc. A, 195, 402.Google Scholar
Keffer, J. F., 1965. “The uniform distortion of a turbulent wake”, J. Fluid Mech., 22, 135.CrossRefGoogle Scholar
Kraichnan, R. H., 1959. “The structure of isotropie turbulence at very high Reynolds numbers”, J. Fluid Mech., 18, 497.CrossRefGoogle Scholar
Leslie, D. C., 1968. Private communication.Google Scholar
Liepmann, H. W., 1961. Free turbulent flows. Mecanique de la Turbulence: Paris, CNRS.Google Scholar
Rivlin, R. S., 1957. “The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids”, Q. Appi. Math., 15, 212.CrossRefGoogle Scholar
Spalding, D. B., 1967. “Heat transfer from turbulent separated flows”, J. Fluid Mech., 27. 97.CrossRefGoogle Scholar
Townsend, A. A., 1956. The structure of turbulent shear flow. Cambridge University Press.Google Scholar
Townsend, A. A., 1966. “The mechanism of entrainment in free turbulent flows”, J. Fluid Mech., 26, 689.CrossRefGoogle Scholar
Tyldesley, J. R., 1969. “Transport phenomena in free turbulent flows”, Int. J. Heat Mass Transfer, 12, 489.CrossRefGoogle Scholar
Tyldesley, J. R., and Silver, R. S., 1968. “The prediction of the transport properties of a turbulent fluid”, Int. J. Heat Mass Transfe., 11, 1325.CrossRefGoogle Scholar
Wieghardt, K., 1945. Addendum to L. Prandtl, “Über ein neues Formelsystem für die ausgebildete Turbulenz”, Nachr. Akad. Wiss. Gottingen (Math.- Phys. Kl.), 23, 14.Google Scholar