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Spectrum of passive scalars of high molecular diffusivity in turbulent mixing

Published online by Cambridge University Press:  28 January 2013

P. K. Yeung  and
K. R. Sreenivasan
P. K. Yeung*
Affiliation:
Schools of Aerospace Engineering, Computational Science and Engineering, and Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
K. R. Sreenivasan
Affiliation:
Department of Physics and Courant Institute of Mathematical Sciences, New York University, NY 10012, USA
*
†Email address for correspondence: pk.yeung@ae.gatech.edu
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Abstract

We consider the mixing of passive scalars transported in turbulent flow, with a molecular diffusivity that is large compared to the kinematic viscosity of the fluid. This particular case of mixing has not received much attention in experiment or simulation even though the first putative theory, due to Batchelor, Howells & Townsend (J. Fluid Mech., vol. 5, 1959, pp. 134–139), is now more than 50 years old. We study the problem using direct numerical simulation of decaying scalar fields in steadily sustained homogeneous turbulence as the Schmidt number (the ratio of the kinematic viscosity of the fluid to the molecular diffusivity of the scalar) is allowed to vary from $1/ 8$ to $1/ 2048$ for two values of the microscale Reynolds number, ${R}_{\lambda } \approx 140$ and $\approx $240. The simulations show that the passive scalar spectrum assumes a slope of $- 17/ 3$ in a range of scales, as predicted by the theory, when the Schmidt number is small and the Reynolds number is simultaneously large. The observed agreement between theory and simulation in the prefactor in the spectrum is not perfect. We assess the reasons for this discrepancy by a careful examination of the scalar evolution equation in the light of the assumptions of the theory, and conclude that the finite range of scales resolved in simulations is the main reason. Numerical issues specific to the regime of very low Schmidt numbers are also addressed briefly.

JFM classification

Mixing: Turbulent mixing Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , R14
Copyright
©2013 Cambridge University Press

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