Hostname: page-component-f554764f5-rvxtl Total loading time: 0 Render date: 2025-04-08T22:55:20.772Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling the behaviour of homogeneous scalar turbulence

Published online by Cambridge University Press:  20 April 2006

G. R. Newman ,
B. E. Launder  and
J. L. Lumley
G. R. Newman
Affiliation:
Brown University AVCO Systems Division, 201 Lowell Street, Wilmington, MA 01887.
B. E. Launder
Affiliation:
University of California at Davis AVCO Systems Division, 201 Lowell Street, Wilmington, MA 01887.
J. L. Lumley
Affiliation:
Brown University Cornell University
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper considers the problem of calculating the statistical characteristics of a passive scalar dispersed by a homogeneous turbulence field. In many turbulent shear flows the time-scale for the evolution of the scalar field is intrinsically related to that of the turbulent velocity field. This is by no means always the case, however, and it is at this more general situation that the present work is aimed. An approximate transport equation for the rate of dissipation of scalar variance is proposed which, it is argued, must contain (at least) two sink terms one of which responds to the time scale of the velocity field while the other reflects that of the scalar field itself. The model has been applied to the limited number of homogeneous scalar flows for which data are available and achieves satisfactory agreement as judged by the evolution of the mean-square scalar variance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 217 - 232
Copyright
© 1981 Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Alexopoulos, C. C. & Keffer, J. F. 1971 Turbulent wake in a passively stratified field. Phys. Fluids 14, 216.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bradshaw, P. 1976 Introduction. In Topics in Applied Physics 12, Turbulence, ch. 1. Springer-Verlag.
Béguier, C., Dekeyser, I. & Launder, B. E. 1978 Ratio of scalar and velocity dissipation time scales in shear flow turbulence. Phys. Fluids 21, 307.Google Scholar
Champagne, F. H., Friehe, C. A., La Rue, J. C. & Wyngaard, J. C. 1977 Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515.Google Scholar
Corrsin, S. 1951 The decay of isotropic temperature fluctuations in an isotropic turbulence. J. Aeron. Sci. 18, 417.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw Hill.
Kraichnan, R. H. 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513.Google Scholar
Launder, B. E. 1975a On the effects of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech. 67, 569.Google Scholar
Launder, B. E. 1975b Progress in the modelling of turbulent transport. Prediction Methods for Turbulent Flows. Notes for Lecture Series No. 76, Von Karman Institute, Rhode-St-Genese, Belgium.
Launder, B. E. 1976 Heat and mass transport. In Topics in Applied Physics 12, Turbulence, ch. 6. Springer-Verlag.
Lin, S. C. & Lin, S. C. 1973 Study of strong temperature mixing in subsonic grid turbulence. Phys. Fluids 16, 1587.Google Scholar
Loitsianskii, L. G. 1939 Some basic laws of isotropic turbulent flow. Cent. Aero. Hydro. Inst., Moscow, Rep. 440 (translation in NACA TM 1079).
Lumley, J. L. 1970a Toward a turbulent constitutive relation. J. Fluid Mech. 41, 413.Google Scholar
Lumley, J. L. 1970b Stochastic Tools in Turbulence. Academic Press.
Lumley, J. L. 1972 A model for computation of stratified turbulent flows. Proc. Intern. Symp. on Stratified Flows, Novosibirsk.
Lumley, J. L. 1975 Introduction. Prediction Methods for Turbulent Flows. Notes for Lecture Series No. 76, Von Karman Institute, Rhode-St-Genese, Belgium.
Lumley, J. L. & Newman, G. R. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161.Google Scholar
Mills, R. R. & Corrsin, S. 1959 Effects of contraction on turbulence and temperature fluctuations generated by a warm grid. NACA Memo 5–5–59W.
Mills, R. R., Kistler, A. L., O'Brien, V. & Corrsin, S. 1958 Turbulence and temperature fluctuations behind a heated grid. NACA TN 4288.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
Newman, G. R. & Herring, J. R. 1979 A test field model study of a passive scalar in isotropic turbulence. J. Fluid Mech. 94, 163.Google Scholar
Saffman, P. G. 1967 The large scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581.Google Scholar
Schumann, H. 1977 Realizability of Reynolds stress models. Phys. Fluids 20, 721.Google Scholar
Spalding, D. B. 1971 Concentration fluctuations in a round turbulent free jet. Chem. Eng. Sci. 26, 95.Google Scholar
Tennekes, H. & Lumley, J. L. 1973 A First Course in Turbulence. MIT Press.
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659.Google Scholar
Webster, C. A. G. 1964 An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech. 19, 221.Google Scholar
Wiskind, H. 1962 J. Geophys. Res. 67, 3033.
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233.Google Scholar
Zeman, O. & Lumley, J. L. 1976 Modeling buoyancy-driven mixed layers. J. Atmos. Sci. 33, 1974.Google Scholar