In order to improve the physical understanding of the development of turbulent structures, the compressible evolution equations for the first three invariants $P$, $Q$ and $R$ of the velocity gradient tensor have been derived. The mean evolution of characteristic turbulent structure types in the $QR$-space were studied and compared at different wall-normal locations of a compressible turbulent boundary layer. The evolution of these structure types is fundamental to the physics that needs to be captured by turbulence models. Significant variations of the mean evolution are found across the boundary layer. The key features of the changes of the mean trajectories in the invariant phase space are highlighted and the consequences of the changes are discussed. Further, the individual elements of the overall evolution are studied separately to identify the causes that lead to the evolution varying with the distance to the wall. Significant impact of the wall-normal location on the coupling between the pressure-Hessian tensor and the velocity gradient tensor was found. The highlighted features are crucial for the development of more universal future turbulence models.
Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer
