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The spectrum of a turbulent passive scalar in the viscous–convective range

Published online by Cambridge University Press:  26 April 2006

J. Qian
J. Qian
Affiliation:
Department of Physics, Graduate School of Academia Sinica, P.O. Box 3908, Beijing 100039, China
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Abstract

The closed equations of isotropic turbulence, obtained by the method of non-equilibrium statistical mechanics and a perturbation-variation approach (Qian 1983, 1985, 1988), are applied to the study of the spectrum dynamics of a turbulent passive scalar in the viscous–convective range. Batchelor's k−1 spectrum is further confirmed. Moreover the effective average value of the least principal rate of strain γ in Batchelor's spectrum function is theoretically evaluated and it is found that γ−1 = C(ν/ε)½ with C = 2√5. Here ν is the kinematic viscosity, and ε is the energy dissipation rate. This prediction is in agreement with experimental data reported by Grant et al. (1968) and Williams & Paulson (1977).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 203 - 212
Copyright
© 1990 Cambridge University Press

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References

Batchelor, G. K. 1959 J. Fluid Mech. 5, 113.
Gibson, C. H. 1968 Phys. Fluids 11, 2316.
Grant, H. J., Hughes, B. A., Vogel, W. M. & Moilliet, A. 1968 J. Fluid Mech. 34, 423.
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Choliet, J. P. & Larcheveque, M. 1982 J. Fluid Mech. 124, 411.
Kraichnan, R. H. 1968 Phys. Fluids 11, 945.
Leslie, D. C. 1973 Developments in The Theory of Turbulence. Clarendon.
Newman, G. R. & Herring, J. R. 1979 J. Fluid Mech. 94, 163.
Orszag, S. A. 1974 In Proc. 1973 Les Houches Summer School (ed. R. Balian & J. L. Peabe). Gordon & Breach.
Pao, Y. H. 1965 Phys. Fluids 8, 1063.
Qian, J. 1983 Phys. Fluids 26, 2098.
Qian, J. 1984 Phys. Fluids 27, 2229.
Qian, J. 1985 Phys. Fluids 28, 1299.
Qian, J. 1987 Acta Mechanica Sinica 19 (2), 174.
Qian, J. 1988 Mechanics and Practice 10, No. 3, 1 (in Chinese).
Reid, W. H. 1955 Proc. Camb. Phil. Soc. 51, 350.
Williams, R. M. & Paulson, C. A. 1977 J. Fluid Mech. 83, 547.