_ Vol. 26 (2) (2000) pp. 95-104 _
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Fluid Dynamics Research, Vol. 26 (2) (2000) pp. 95-104
© 2000 The Japan society of Fluid Mechanics and and Elsevier Science B.V. All rights reserved.
PII: S0169-5983(99)00016-7

Isotropic and axisymmetric turbulence of passive scalars

B.K. Shivamoggi1 * and R.A. Antonia

University of Newcastle, Newcastle, NSW 2308, Australia

Received 31 August 1998; received in revised form 15 December 1998; accepted 25 March 1999

Abstract

A statistical approach to isotropic/axisymmetric turbulence of passive scalars is considered. The scalar transport equation provides Kármán-Howarth-type equations governing the scalar functions that characterize the statistical correlations of flow properties. These equations admit Loitsiansky-type integrals which may be interpreted via the generation of equipartition spectra for the scalar variance for small wavenumbers. These Kármán-Howarth-type equations are used to deduce the behavior of the scalar autocorrelation for small r. It is possible to deduce a Yaglom-like equation also for the axisymmetric case, and to give it a simple interpretation as in the isotropic case.

1 Permanent address: University of Central Florida, Department of Mathematics, P.O. Box 161364, Orlando, FL 32816, USA.

*Corresponding author. Fax: +1 407 823 6253.

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