On the Reynolds number dependence of velocity-gradient structure and dynamics

We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number (Re-lambda). The analysis factorizes the velocity gradient (A(ij)) into the magnitude (A(2)) and normalized-gradient tensor (b(ij) = A(ij)/root A(2)). The focus is on bounded b(ij) as (i) it describes small-scale structure and local streamline topology, and (ii) its dynamics is shown to determine magnitude evolution. Using direct numerical simulation (DNS) data, the moments and probability distributions of b(ij) and its scalar invariants are shown to attain Re-lambda independence. The critical values beyond which each feature attains Re-lambda independence are established. We proceed to characterize the Re-lambda dependence of b(ij)-conditioned statistics of key non-local pressure and viscous processes. Overall, the analysis provides further insight into velocity-gradient dynamics and offers an alternative framework for investigating intermittency, multifractal behaviour and for developing closure models.