Previous studies on stratified shear layers involving two streams with different densities have been conducted under the Boussinesq approximation, while the combined effect of stratified instability and mean shear in relation to multi-layer density stratification induced by scalar fields remains an unresolved fundamental question. In this paper, the shear-driven mixing flow involving initial double-layer density interfaces due to the compositional differences are numerically investigated, in which the mean shear interacts with Rayleigh–Taylor instability (RTI). Since its critical role in dynamics of shear layers and scalar transport, we focus on the evolution of entrophy and vortical structures. We find that the dynamics of mixing layers are determined by the mean shear and the distance between the initial density stratification. The mean shear and the Kelvin–Helmholtz instability dominate the evolution of shear layers at the initial stage. The increase in mean shear, therefore, is favorable for turbulent mixing, irrespective of effect of RTI. However, once the transition of turbulence occurs, the mean shear becomes weaker and RTI becomes prominent. This promotes the destruction of hairpin vortex and generation of vortex tube. In addition, the interaction of mean shear with RTI becomes weaker with increasing distance between initial density stratification. Furthermore, the viscous dissipation of enstrophy is larger than enstrophy production in the turbulent region due to the effect of RTI. The baroclinic term has the larger contribution in the turbulent region than near the turbulent/non-turbulent interface, which is different from the results of stably stratified flow under the Boussinesq approximation.

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