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

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.