Velocity gradient partitioning in turbulent flows

A normality-based triple decomposition of the velocity gradient tensor reveals contributions from three distinct modes of deformation: axial straining, rigid rotation, and pure shearing. We use this decomposition to partition the strength of velocity gradient fluctuations in several canonical turbulent flows, including forced isotropic turbulence, channels and boundary layers, and subsonic and transonic jets. For forced isotropic turbulence, the partitioning agrees well with previous results. For the wall-bounded flows, 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 reasonably well as a function of the mean shearing strength. For the turbulent jets, the isotropic partitioning applies broadly due to the rapid decay of the shear layer near the nozzle lip. Before reaching the potential flow regime, the partitioning near the turbulent/non-turbulent interface is associated with an enhanced relative contribution from rigid rotation. Given our results, the velocity gradient partitioning shows promise for modeling a broad class of turbulent flows.