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Analogy between velocity and scalar fields in a turbulent channel flow

Published online by Cambridge University Press:  01 June 2009

ROBERT ANTHONY ANTONIA ,
HIROYUKI ABE  and
HIROSHI KAWAMURA
ROBERT ANTHONY ANTONIA*
Affiliation:
Discipline of Mechanical Engineering, University of Newcastle, NSW 2308, Australia
HIROYUKI ABE
Affiliation:
Japan Aerospace Exploration Agency, Tokyo 182-8522, Japan
HIROSHI KAWAMURA
Affiliation:
Department of Mechanical Engineering, Tokyo University of Science, Chiba 278-8510, Japan
*
†Email address for correspondence: [email protected]
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Abstract

The relationship between the fluctuating velocity vector and the temperature fluctuation has been examined using direct numerical simulation databases of a turbulent channel flow with passive scalar transport using a constant time-averaged heat flux at each wall for h+ = 180, 395, 640 and 1020 (where h is the channel half-width with the superscript denoting normalization by wall variables) at Prandtl number Pr=0.71. The analogy between spectra corresponding to the kinetic energy and scalar variance is reasonable in both inner and outer regions irrespective of whether the spectra are plotted in terms of kx or kz, the wavenumbers in the streamwise and spanwise directions respectively. Whereas all three velocity fluctuations contribute to the energy spectrum when kx is used, the longitudinal velocity fluctuation is the major contributor when kz is used. The quality of the analogy in the spectral domain is confirmed by visualizations in physical space and reflects differences between spatial organizations in the velocity and scalar fields. The similarity between the spectra corresponding to the enstrophy and scalar dissipation rate is not as good as that between the kinetic energy and scalar variance, emphasizing the prominence of the scalar sheets as the centre of the channel is approached. The ratio R between the characteristic time scales of the velocity and scalar fluctuations is approximately constant over a major part of the channel and independent of h+, when the latter is sufficiently large. This constancy, which is not observed in quantities such as the turbulent Prandtl number, follows from the spectral similarities discussed in this paper and has implications for turbulent heat transport models.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 241 - 268
Copyright
Copyright © Cambridge University Press 2009

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References

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