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The diffusion of scalar and vector fields by homogeneous stationary turbulence

Published online by Cambridge University Press:  12 April 2006

Edgar Knobloch
Edgar Knobloch
Affiliation:
Harvard College Observatory, 60 Garden Street, Cambridge, Massachusetts 02138
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Abstract

An exact Eulerian formulation of the problem of diffusion of passive scalar and vector fields by a turbulent velocity field is obtained. It is shown that, in the short autocorrelation time limit, the diffusion equation is exact for any turbulence. For non-zero autocorrelation times the form of the first few correction terms to the diffusion equation is found. As a result of these corrections the diffusion of scalar, divergence-free and curl-free vector fields will be different. The calculations use the Kubo–Van Kampen–Terwiel technique and are carried out for zero ordinary diffusivity and for homogeneous, stationary, isotropic, incompressible, helical turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 1 , 1 November 1977 , pp. 129 - 140
Copyright
© 1977 Cambridge University Press

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References

Balescu, R. & Misguich, J. H. 1975 J. Plasma Phys. 13, 33.
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1959 J. Fluid Mech. 5, 113.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bourret, R. C. 1962a Can. J. Phys. 40, 782.
Bourret, R. C. 1962b Nuovo Cimento 26, 1.
Bourret, R. C. 1965 Can. J. Phys. 43, 6.
Brissaud, A. & Frisch, U. 1974 J. Math. Phys. 15, 524.
Kazantsev, A. D. 1968 Sov. Phys. J. Exp. Theor. Phys. 26, 1031.
Kraichnan, R. H. 1961 J. Math. Phys. 2, 124.
Kraichnan, R. H. 1966 Phys. Fluids 9, 1728, 1884, 1937.
Kraichnan, R. H. 1968 Phys. Fluids 11, 945.
Kraichnan, R. H. 1976a J. Fluid Mech. 75, 657.
Kraichnan, R. H. 1976b J. Fluid Mech. 77, 753.
Kubo, R. 1963 J. Math. Phys. 4, 174.
Moffatt, H. K. 1970 J. Fluid Mech. 41, 435.
Moffatt, H. K. 1972 In Statistical Methods and Turbulence, Lecture Notes in Physics, vol. 12, p. 266. Springer.
Moffatt, H. K. 1974 J. Fluid Mech. 65, 1.
Parker, E. N. 1971 Astrophys. J. 163, 279.
Roberts, P. H. 1961 J. Fluid Mech. 11, 257.
Saffman, P. G. 1963 J. Fluid Mech. 16, 545.
Terwiel, R. H. 1974 Physica 74, 248.
Vainshtein, S. I. 1970 Sov. Phys. J. Exp. Theor. Phys. 31, 87.
Vainshtein, S. I. 1972 Sov. Phys. J. Exp. Theor. Phys. 34, 327.
Vainshtein, S. I. & Zel'dovich, Ya. B. 1972 Sov. Phys. Uspekhi 15, 159.
Van Kampen, N. G. 1974a Physica 74, 215.
Van Kampen, N. G. 1974b Physica 74, 239.
Van Kampen, N. G. 1976 Phys. Rep. 24, 171.
Weinstock, J. 1969 Phys. Fluids 12, 1045.