This report describes the work carried out in `universality' aspects of the dynamics of turbulence in compressible flows. Direct numerical simulations (DNSs) are carried out in different inhomogeneous and anisotropic flows. All discussed flows show regions of strong imbalance of turbulent production and turbulent dissipation. This distinguishes this work from most studies in the literature about the fundamentals of turbulent dynamics. A characteristic decomposition in addition to temporal and spatial filtering are applied as tools to compare differences in the turbulent dynamics across different flow topologies. The work includes a discussion about universal aspects of the velocity gradient and related quantities in a turbulent boundary layer, in a jet flow as well as in a wake flow. Invariant features are highlighted and quantified and the differences are pointed out. The velocity gradient and the enstrophy production, as one of the key quantities in the turbulent energy cascading process, are discussed in great detail in the turbulent boundary layer flow. Focus hereby is on the wall-normal development of the structure of the enstrophy production. This is followed by a comprehensive overview of a turbulent boundary layer. This includes the presentation and discussion of global energy redistributing mechanisms from different perspectives. The key role of turbulence in these processes is made clear. The energy cascade is dissected at different locations which reveals three different transfer processes. Two of which are transferring energy from larger scales of motion towards smaller scales of motion. In addition a backscatter mechanism was discovered that transfers energy from smaller scales towards larger scales of motion. Besides this some specific and potentially universal features of turbulence within the turbulent boundary layer results are discussed.