Transition to Self-Similarity of Diffusion of Tracer in Turbulent Patch
Publication: Journal of Engineering Mechanics
Volume 127, Issue 11
Abstract
A mixing of a passive tracer inside a turbulent patch generated by a localized short-time perturbation is studied numerically and analytically. Two kinds of an initial distribution of a tracer are considered: two-layer and continuous with constant gradient. For the turbulent patch shaped as a layer, it is shown that, regardless of details of initial distributions of a turbulent energy and dissipation, a tracer concentration evolves to self-similar regimes as time elapses. Analytical self-similar solutions to turbulent diffusion equations are found for three symmetric shapes of a turbulent patch: layer, cylinder, and sphere. Distributions of the concentration inside a patch are found to be substantially nonuniform, with a typical ratio of a concentration gradient in the middle of a patch to its initial value of about 0.5.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barenblatt, G. I. ( 1996). Scaling, self-similarity, and intermediate asymptotics, Cambridge University Press, London.
2.
Barenblatt, G. I., Galerkina, N. L., and Luneva, M. V. ( 1987). “Evolution of a turbulent burst.” J. Engrg. Phys., London, 53(5), 1246–1252.
3.
Frost, W. and Moulden, T.H., eds. ( 1977). Handbook of turbulence. Fundamentals and applications, Plenum, New York.
4.
Hanjalic, K., and Launder, B. E. ( 1972). “A Reynolds stress model of turbulence and its application to thin shear flows.” J. Fluid Mech., Cambridge, U.K., 52, 609–638.
5.
Kamke, E. ( 1965). Differentialgleichungen, Akademische Verlagsgesellschaft, Leipzig, Germany (in German).
6.
Launder, B. E., and Spalding, D. B. ( 1974). “The numerical computation of turbulent flow.” Comp. Methods in Appl. Mech. and Engrg., Amsterdam, 3(1), 269–289.
7.
Monin, A. S., and Ozmidov, R. V. ( 1985). Turbulence in the ocean, Reidel, Boston.
8.
Monin, A. S., and Yaglom, A. M. ( 1971). Statistical fluid mechanics. Mechanics of turbulence, Vol. 1, MIT Press, Cambridge, Mass.
9.
Reynolds, W. C. ( 1976). “Computation of turbulent flows.” Annu. Rev. Fluid Mech., 8, 183–203.
10.
Speziale, C. G. ( 1991). “Analytical methods for the development of Reynolds-stress closures in turbulence.” Annu. Rev. Fluid Mech., 23, 107–157.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 127 • Issue 11 • November 2001
Pages: 1089 - 1095
History
Received: Jul 10, 2000
Published online: Nov 1, 2001
Published in print: Nov 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.