Velocity gradient partitioning in turbulent flows

The velocity gradient tensor can be decomposed into axial straining, pure shearing, and rigid rotation tensors, each with distinct symmetry and normality properties. We partition the strength of velocity gradient fluctuations based on the relative contributions of these constituents in several turbulent flows. These flows include forced isotropic turbulence, channels and boundary layers, and subsonic and transonic jets. For forced isotropic turbulence, the partitioning is in excellent agreement with previous results. For wall-bounded turbulence, the partitioning collapses onto the isotropic partitioning far from the wall, where the mean shearing is relatively weak. By contrast, the near-wall partitioning is dominated by shearing. Between these two regimes, the partitioning collapses well at sufficiently high friction Reynolds numbers and its variations in the buffer layer and the log-law region can be reasonably modeled as a function of the mean shearing strength. The isotropic partitioning also applies throughout much of the turbulent jets due to the rapid decay of the mean flow shear layer near the nozzle lip. Before reaching the exterior potential flow regime, the relative contribution of rigid rotation around the turbulent/non-turbulent interface is enhanced with respect to the isotropic partitioning. Altogether, our results highlight the broad applicability of the velocity gradient partitioning to turbulence modeling.