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Influences of small-scale shear instability on passive-scalar mixing in a shear-free turbulent front

Published online by Cambridge University Press:  02 April 2025

Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window]  and
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]
Tomoaki Watanabe*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615–8540, Japan
Koji Nagata
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615–8540, Japan
*
Corresponding author: Tomoaki Watanabe, [email protected]
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Abstract

Local shearing motions in turbulence form small-scale shear layers, which are unstable to perturbations at approximately 30 times the Kolmogorov scale. This study conducts direct numerical simulations of passive-scalar mixing layers in a shear-free turbulent front to investigate mixing enhancements induced by such perturbations. The initial turbulent Reynolds number based on the Taylor microscale is $ Re_\lambda = 72$ or 202. The turbulent front develops by entraining outer fluid. Weak sinusoidal velocity perturbations are introduced locally, either inside or outside the turbulent front, or globally throughout the flow. Perturbations at this critical wavelength promote small-scale shear instability, complicating the boundary geometry of the scalar mixing layer at small scales. This increases the fractal dimension and enhances scalar diffusion outward from the scalar mixing layer. Additionally, the promoted instability increases the scalar dissipation rate and turbulent scalar flux at small scales, facilitating faster scalar mixing. The effects manifest locally; external perturbations intensify mixing near the boundary, while internal perturbations affect the entire turbulent region. The impact of perturbations is consistent across different Reynolds numbers when the amplitudes normalised by the Kolmogorov velocity are the same, indicating that even weaker perturbations can enhance scalar mixing at higher Reynolds numbers. The mean scalar dissipation rate increases by up to 50 %, even when the perturbation energy is only 2.5 % of the turbulent kinetic energy. These results underscore the potential to leverage small-scale shear instability for efficient mixing enhancement in applications such as chemically reacting flows.

JFM classification

Mixing: Turbulent mixing Wakes/Jets: Shear layers
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A20
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© The Author(s), 2025. Published by Cambridge University Press

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