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A random-flight evaluation of the constants of relative dispersion in idealized turbulence

Published online by Cambridge University Press:  26 April 2006

Alan J. Faller
Alan J. Faller
Affiliation:
78 Bellevue Ave., Melrose, MA 02176, USA
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Abstract

In the idealized problem of homogeneous isotropic stationary inertial-range turbulence the rate of relative dispersion of an ensemble of tracer pairs can be characterized by a constant C0. In order to compute this constant with random-flight equations, however, it is necessary first to know the values of two other constants, C1 and C2, that occur in the two-particle velocity-component relations of Lagrangian tracers (Faller 1992).

C1 and C2 are found by an elaborate trial and error procedure in a new two-tracer random-flight model of dispersion that matches input and output values of these two variates. The constant C0 is then computed using the Lagrangian relations and is found to be significantly smaller than when the Eulerian Kármán/Howarth correlations are used.

The probability density distribution of tracer separations has a kurtosis slightly larger than that of a comparable Gaussian distribution. At small spacings the frequency of tracer spacings is six to ten times larger than would be expected from a Gaussian distribution. The distribution function for the speed of separation of the Lagrangian tracers has a negative skewness similar to that found for two-point Eulerian velocities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 316 , 10 June 1996 , pp. 139 - 161
Copyright
© 1996 Cambridge University Press

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References

Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Borgas, M. S. & Sawford, B. L. 1994 A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence. J. Fluid Mech. 279, 69–99.Google Scholar
Corrsin, S. 1963 Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. J. Atmos. Sci. 20, 115–119.Google Scholar
Dickey, T. D. & Mellor, G. L. 1979 The Kolmogoroff r2/3 law. Phys. Fluids 22, 1029–1032.Google Scholar
Dop, H. VAN & Nieuwstadt, F. T. M. 1985 Random walk models for particle displacements in inhomogeneous, unsteady turbulent flows. Phys. Fluids 28, 1639–1653.Google Scholar
Durbin, P. A. 1980 A random-flight model of inhomogeneous turbulent dispersion. Phys. Fluids 23, 2151–2153.Google Scholar
Durbin, P. A. 1983 Stochastic differential equations and turbulent dispersion. Natl Aero. & Space Admin. Reference Publ. 1103.
Faller, A. J. 1992 Approximate second-order two-point velocity relations for turbulent dispersion. J. Fluid Mech. 244, 713–720.Google Scholar
Faller, A. J & Auer, S. J. 1988 The role of Langmuir circulations in the dispersion of surface tracers. J. Phys. Oceanogr. 18, 1108–1123.Google Scholar
Faller, A. J. & Choi, G.-S. 1985 Random-flight studies of relative dispersion in homogeneous and isotropic two- and three-dimensional turbulence. Tech. Note Bn-1035. Inst. for Phys. Sci. and Tech., Univ. of Maryland.
Kármán, T. VON & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164, 192–215.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics. MIT Press.
Richardson, L. F. 1926 Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond. A 110, 709–737.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. (2) 20, 1196.Google Scholar
Tennekes, H. & Lumley, J. S. 1972 A First Course in Turbulence. MIT Press.
Thomson, D. J. 1986 A random walk model of dispersion in turbulent flows and its application to dispersion in a valley. Q. J. R. Met. Soc. 112, 511–530.Google Scholar
Thomson, D. J. 1987 Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180, 529–556.Google Scholar
Thomson, D. J. 1990 A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance. J. Fluid. Mech. 210, 113–153.Google Scholar