Statistical Breakdown of Numerically Simulated Shear-Free Flows

A statistical analysis of several DNSs of incompressible turbulent shear-free flows (with Reλ ranging from ≈ 86 to ≈ 245) was performed, aimed to study the small scale processes that promote turbulent entrainment at the TNTI. After a certain transient, the shearless flows reached a statistically steady state. From that time instant, the main features of the various flow configurations were statistically investigated by assessing the classical and conditional mean profiles of total kinetic energy (K) and anisotropy ratio (urms/ξ), the classical and conditional mean profiles of the terms of the total kinetic energy budget (advection C, pressure strain Π, viscous diffusion Dv, dissipation ε and power injection Pi), the classical PDFs of the velocity components (u, v and w), the classical and conditional mean profiles of the invariants of the velocity gradient (R and Q), rate-of-strain (RS and QS) and rate-of-rotation (QW) tensors and the classical and conditional J PDFs of the same invariants. Conditional statistical quantities were computed in relation to the distance from the TNTI. To avoid the accidental mixing of turbulent and non-turbulent points in the conditional statistics, all the nodes belonging to irrotational bubbles and turbulent islands were neglected. All the conditional mean profiles are characterized by very sharp gradients at the TNTI, meanwhile in the classical mean profiles the variations are distributed on a much wider portion of the domain, indicating how the conditional averages are able to successfully discern turbulent and irrotational regions, avoiding the smoothening of the mean profiles via large scale intermittency. The similarity between the conditional statistics obtained here for shearless flows, and those extracted from temporal jets in previous works, is very interesting, since it suggests some sort of universality in the TNTI dynamics, as well asin the turbulent entrainment processes.