Study of the vortex structure in compressible wall-bounded turbulence

The similarity of turbulent structures between compressible and incompressible wall turbulence has been well recognized through mostly visualization of instantaneous fields. However, some questions remain unclear, such as will Morkovin's hypothesis and semilocal scaling, with which many mean flow profiles collapse, also be applicable to instantaneous features of turbulence structures and why. The present work dissects features of vortical structures in compressible channel flows comprehensively to address these questions by employing the direct numerical simulations database of turbulent channel flows covering broad Mach and Reynolds numbers. Most features investigated show satisfactory agreement quantitatively with the incompressible counterparts in semilocal units, which indicates the validity of Morkovin's hypothesis based on the semilocal scaling. This observation extends Morkovin's hypothesis from standard mean flow statistics to instantaneous vortex features and suggests that the dominant mechanism governing vortex evolution remains the same as incompressible flows. Specifically, the streamwise vortex inclination angle approaches 45 degrees as the wall-normal distance grows, which is supported by a theoretical estimation extended from incompressible flows by claiming the compressibility does not alter the vortex orientation. Regarding the size and strength of vortices, the average radius of vortices grows with the wall-normal distance, while the average strength becomes weaker. The vortex population increases with Reynolds number evidently, while it decreases marginally with Mach numbers. It is impressive that the population percentage of different types of vortices is similar to all the cases in the near-wall region. Last, a heuristic model is developed as a potential candidate for describing the topology of instantaneous vortices. In cooperation with the topological model, these statistical results could be crucial input references to reconstruct flow fields using vortex methods.