Velocity-Vorticity Correlation Structure (VVCS) in Transitional Compressible Turbulent Boundary Layer

Velocity-vorticity correlation structure (VVCS) is used to measure the geometry of vortices in the numerically simulated compressible boundary layer (BL) at Ma=2.25, 4.5, and 6.0. Wall normal vorticity represented by $VVCS_{12}$ corresponds to the low-speed streaks, flanked by counter-rotating streamwise vortices identified by $VVCS_{11}$. The ratio of spanwise size to spanwise spacing of $VVCS_{12}$ decreases from 3 to unity during transition to turbulence, indicating low-speed streaks gradually populating in $x$. During transition, correlation coefficient, R$_{ij}$ near the wall decreases at first then increases up to 0.55, indicating that the well-arranged hairpins break up into streamwise vortices, as observed in visualization of this region. At each $y$, the length of spanwise vortices identified by VVCS$_{13}$ decreases fast during transition at all $Ma$s, indicating thickening of BL, while becoming nearly invariant in $x$ in the well-developed region, consistent with a self-similar turbulent BL predicted by our theory (She2018JFM). For both $VVCS_{11}$ and $VVCS_{12}$ the spanwise size equals the transverse size in the developed flow region. These results affirm the predominant role of the multi-layered structure and suggest new possibilities for control of turbulent flow.