Velocity-vorticity correlation structures (VVCS) in spatially developing compressible turbulent boundary layer

A velocity-vorticity correlation structure (VVCS) analysis is applied to the direct numerical simulation (DNS) of compressible turbulent boundary layer (CTBL) at Mach numbers, $Ma=2.25$, $4.50$ and $6.0$. It is shown that the VVCS analysis captures the geometry variation in the streamwise direction during the transition and in the wall-normal direction in the fully developed regime. Specifically, before transition, the VVCS captures the instability wave number, while in the transition region it displays a distinct scaling change of the dimensions. The fully developed turbulence regime is characterized by a nearly constant spatial extension of the VVCS. Particularly, after turbulence is well developed, a multi-layer structure in the wall normal direction is observed in the maximum correlation coefficient and in the length scales of the VVCS, as expected from a recent symmetry-based theory, the ensemble structure dynamics (SED). The most interesting outcome is an observed linear dependence of the length scale of the VVCS from $y^+\approx50$ to $200$, which is a direct support to Townsend’s attached-eddy theory. In conclusion, the VVCS analysis quantifies the geometrical characteristics of the coherent structures in turbulent compressible shear flows throughout the whole domain.