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Measurements of concentration fluctuations in relative turbulent diffusion

Published online by Cambridge University Press:  19 April 2006

P. C. Chatwin  and
Paul J. Sullivan
P. C. Chatwin
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Liverpool
Paul J. Sullivan
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Liverpool Permanent address: Department of Applied Mathematics, University of Western Ontario, London, Canada.
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Abstract

In 1965 Sullivan made many measurements of concentration in dye plumes in the surface layer of Lake Huron with the primary purpose of estimating the distance–neighbour function (Sullivan 1965, 1971). This paper presents the results of a recent analysis of the concentration fluctuations in these experiments for, despite their great practical and theoretical importance, there are very few published reports of such measurements from natural environments. One reason for this apparent neglect has undoubtedly been the anticipated high noise level, and the present results confirm this expectation. The experimental analysis uses the framework of relative diffusion since this has great advantages compared with that of absolute diffusion. Despite the noise, the results are consistent, to the degree of spatial resolution attained, with the self-similar structure anticipated for relative, but not absolute, diffusion. Further interesting features of the results are that changes in the form of the statistical properties across the plume indicate an unexpectedly strong influence of the central regions, and that certain statistical properties have much less noisy profiles than that of the mean square fluctuations. The influence of molecular diffusion is shown to be strong. Interpretation of the results is based partly on the extension of the theory recently developed by Chatwin & Sullivan (1979a) for a cloud, although the limited spatial resolution attained did not allow direct critical examination of this work.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 1 , 11 September 1979 , pp. 83 - 101
Copyright
© 1979 Cambridge University Press

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References

Batchelor, G. K. 1952a Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345.Google Scholar
Batchelor, G. K. 1952b The effect of homogeneous turbulence on material lines and surfaces. Proc. Roy. Soc. A 213, 349.Google Scholar
Batchelor, G. K. 1959 Small-scale variations of convected quantities like temperature in turbulent fluid. Part I. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113.CrossRefGoogle Scholar
Chatwin, P. C. & Sullivan, P. J. 1979a The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow. J. Fluid Mech. 91, 337.Google Scholar
Chatwin, P. C. & Sullivan, P. J. 1979b Some diffusion invariants. Submitted to J. Fluid Mech.Google Scholar
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469.Google Scholar
Crum, G. F. & Hanratty, T. J. 1965 Dissipation of a sheet of heated air in a turbulent flow. App. Sci. Res. A 15, 177.Google Scholar
Csanady, G. T. 1963 Turbulent diffusion in Lake Huron. J. Fluid Mech. 17, 360.Google Scholar
Csanady, G. T. 1973 Turbulent Diffusion in the Environment. Dordrecht: D. Reidel Publishing Company..
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, Volume 2 (ed. by J. L. Lumley). The M.I.T. Press.
Murthy, C. R. & Csanady, G. T. 1971 Experimental studies of relative diffusion in Lake Huron. J. Phys. Ocean. 1, 17.Google Scholar
Obukhoff, A. M. 1949 Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk S.S.S.R. Geogr. i Geofiz. 13, 58.Google Scholar
Sullivan, P. J. 1965 A description of the relative turbulent diffusion of a cloud of marked fluid elements using a distance neighbour function. M.A.Sc. Thesis, University of Waterloo.
Sullivan, P. J. 1971 Some data on the distance—neighbour function for relative diffusion. J. Fluid Mech. 47, 601.Google Scholar
Sullivan, P. J. 1975 The 4/3rds. law of relative diffusion. Mém. Soc. Roy. Sci. Liège, 6e. série 7, 253.Google Scholar
Uberoi, M. S. & Corrsin, S. 1953 Diffusion of heat from a line source in isotropic turbulence. N.A.C.A. Rep. 1142.Google Scholar