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New scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

Published online by Cambridge University Press:  20 July 2020

Hamed Sadeghi Open the ORCID record for Hamed Sadeghi [Opens in a new window]  and
Martin Oberlack Open the ORCID record for Martin Oberlack [Opens in a new window]
Hamed Sadeghi
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, ON K1N 6N5, Canada Chair of Fluid Dynamics, TU Darmstadt, Otto-Bernd-Strasse 2, 64287Darmstadt, Germany
Martin Oberlack*
Affiliation:
Chair of Fluid Dynamics, TU Darmstadt, Otto-Bernd-Strasse 2, 64287Darmstadt, Germany Centre for Computational Engineering, TU Darmstadt, Dolivostrasse 15, 64293Darmstadt, Germany
*
†Email address for correspondence: oberlack@fdy.tu-darmstadt.de
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Abstract

We use the Lie symmetry theory to derive new scaling laws for passive scalar dynamics under the influence of a constant mean gradient of the scalar in decaying homogeneous isotropic turbulence. For this purpose, we apply symmetry analysis to the equations for two-point correlation of the scalar and velocity fluctuations. It is shown that, in contrast to the classical self-similarity approach, the general invariant solutions, respectively scaling laws, of the two-point functions are constructed using the symmetry approach, without requiring an a priori set of similarity scales to carry on the analysis. In the context of the current analysis also, scaling laws for one-point quantities of the scalar variance $\overline{\unicode[STIX]{x1D703}^{2}}$, the transverse scalar flux $\overline{u_{2}\unicode[STIX]{x1D703}}$ and the variance of the turbulent velocity fluctuations $\overline{u^{2}}$ are established, which are essentially related to the scaling symmetries. A key step to derive the scaling laws is the symmetry breaking induced by the constant mean scalar gradient. We use the results of a highly resolved direct numerical simulation of Gauding et al. (Comput. Fluids, vol. 180, 2019, pp. 206–217) to verify the scaling laws and the self-similarity of the two-point correlation functions. It is shown that the general symmetry solutions obtained from symmetry results provide a very good similarity to these functions.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A10
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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