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Structure of iso-scalar sets

Published online by Cambridge University Press:  17 May 2022

M. Gauding ,
F. Thiesset Open the ORCID record for F. Thiesset [Opens in a new window] ,
E. Varea  and
L. Danaila
M. Gauding
Affiliation:
CORIA, UMR 6614, CNRS, Normandy Univ., UNIROUEN, INSA Rouen, 76000 Rouen, France
F. Thiesset*
Affiliation:
CORIA, UMR 6614, CNRS, Normandy Univ., UNIROUEN, INSA Rouen, 76000 Rouen, France
E. Varea
Affiliation:
CORIA, UMR 6614, CNRS, Normandy Univ., UNIROUEN, INSA Rouen, 76000 Rouen, France
L. Danaila
Affiliation:
University of Rouen Normandy, CNRS, M2C, 76000 Rouen, France
*
†Email address for correspondence: [email protected]
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Abstract

An analytical framework is proposed to explore the structure and kinematics of iso-scalar fields. It is based on a two-point statistical analysis of the phase indicator field which is used to track a given iso-scalar volume. The displacement speed of the iso-surface, i.e. the interface velocity relative to the fluid velocity, is explicitly accounted for, thereby generalizing previous two-point equations dedicated to the phase indicator in two-phase flows. Although this framework applies to many transported quantities, we here focus on passive scalar mixing. Particular attention is paid to the effect of Reynolds (the Taylor based Reynolds number is varied from 88 to 530) and Schmidt numbers (in the range 0.1 to 1), together with the influence of flow and scalar forcing. It is first found that diffusion in the iso-surface tangential direction is predominant, emphasizing the primordial influence of curvature on the displacement speed. Second, the appropriate normalizing scales for the two-point statistics at either large, intermediate and small scales are revealed and appear to be related to the radius of gyration, the surface density and the standard deviation of mean curvature, respectively. Third, the onset of an intermediate ‘scaling range’ for the two-point statistics of the phase indicator at sufficiently large Reynolds numbers is observed. The scaling exponent complies with a fractal dimension of 8/3. A scaling range is also observed for the transfer of iso-scalar fields in scale space whose exponent can be estimated by simple scaling arguments and a recent closure of the Corrsin equation. Fourth, the effects of Reynolds and Schmidt numbers together with flow or scalar forcing on the different terms of the two-point budget are highlighted.

JFM classification

Mathematical Foundations: General fluid mechanics Turbulent Flows: Turbulence theory Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A14
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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