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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

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