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Wave and vortex structures in transitional mixing layers: a numerical investigation

Published online by Cambridge University Press:  08 October 2025

Junlin Chen ,
Xianyang Jiang Open the ORCID record for Xianyang Jiang [Opens in a new window]  and
Zuoli Xiao Open the ORCID record for Zuoli Xiao [Opens in a new window]
Junlin Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China
Xianyang Jiang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK
Zuoli Xiao*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China HEDPS and Center for Applied Physics and Technology, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China
*
Corresponding author: Zuoli Xiao, z.xiao@pku.edu.cn
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Abstract

Laminar–turbulent transition in shear flow is complicated and follows many possible routes. In this study, we seek to examine a scenario based on three-dimensional (3-D) waves (Jiang et al., 2020, J. Fluid Mech., vol. 890, A11) in compressible mixing layers, and elucidate the role of 3-D waves in generating streamwise vorticity. The Eulerian–Lagrangian coupled method is used to track the evolution of flow structures. Qualitative evidence shows that localised 3-D waves travel coherently with vortex structures at the early transition stage, which is consistent with the behaviours of 3-D waves in boundary layer transitions. To examine the local flow events surrounding 3-D waves and investigate the cause and effect relationships inherent in wave–vortex interaction, the finite-time Lyapunov exponent and components of the strain rate tensor are integrated into evolving Lagrangian material surfaces. The formation of high-shear layers in the flanks of the 3-D waves is observed, driven by fluid ejection and sweep motions induced by the amplification of 3-D waves. The $\Lambda$-shaped vortices are found born in the vicinity of high-shear regions and then stretched into hairpin-shaped vortices farther downstream. Statistical findings reveal that streamwise vorticity develops concurrently with the significant growth of the oblique mode, while the normal motion of wave structures induces a high strain rate layer in the surrounding region. In addition, conditional statistics underscore the significance of high shear in enstrophy generation. Finally, a conceptual model is proposed to depict the evolution of coherent structures based on the relationship among the 3-D waves, high-shear/strain layers, and $\varLambda$-vortices, providing insights into their collective dynamics within transitional mixing layers.

JFM classification

Instability: Transition to turbulence Turbulent Flows: Shear layer turbulence Turbulent Flows: Wave-turbulence interactions

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A48
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© The Author(s), 2025. Published by Cambridge University Press

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