Turbulent/nonturbulent interface in a spatially evolving compressible turbulent boundary layer

The relationship between the viscous superlayer (VSL) and the pure shear layer (PSL) in a spatially evolving compressible turbulent boundary layer at a Mach number Ma∞=2.9 is analyzed using direct numerical simulation. The geometric characteristics of the outer edge of the turbulent/nonturbulent interface (TNTI) are also investigated. The vorticity ω is decomposed into the shear motions S and rigid rotational motions R based on the Liutex decomposition. Visual analysis reveals the existence of continuous PSL with |ω|=|S| and |R|=0 near the irrotational boundary. A novel identification method based on the Liutex decomposition is used to detect the VSL, which shows that the local scale of the PSL is slightly different from that of the VSL. The mean thickness of the PSL ⟨δPSL⟩I is close to that of the VSL. The local mean curvature H is discussed through multi-scale analysis. A large part of the TNTI has convex shapes with small positive local mean curvature, while the average local mean curvature H¯ is a negative value. This demonstrates the significant effect of extreme negative H events on the geometry of the TNTI. Moreover, H¯ tends to be constant when the TNTI is fully developed. The scale dependence analysis of H¯Δ indicates that H¯Δ exhibits a power-law behavior with filter sizes Δ. As the filter size Δ increases, H¯Δ remains negative and −H¯Δ gradually decreases.