The invariants of the velocity gradient ($R$ and $Q$ ), rate-of-strain ($R_S$ and $Q_S$ ), and rate-of-rotation $\left(Q_W\right)$ tensors are analyzed across the turbulent/nonturbulent (T/NT) interface by using a direct numerical simulation (DNS) of a turbulent plane jet at ${\mathrm{Re}}_{\lambda }\approx 120$ . The invariants allow a detailed characterization of the dynamics, geometry and topology of the flow during the entrainment. The invariants $Q$ and $Q_S$ are almost equal and negative outside the turbulent region close to the T/NT interface, which shows the existence of high values of strain product (hence viscous dissipation of kinetic energy) at that location. Right at the T/NT interface, the invariants $Q_W$ and $Q_S$ show that virtually all flow points there are characterized by irrotational dissipation, with no discernible sign of the coherent structures which are known to exist deep inside the turbulent region. Moreover, the invariants of the velocity gradient tensor ($Q$ and $R$ ) show that the classical “teardrop” shape of their associated phase map is not yet formed at the T/NT interface. All the invariants rapidly change after the T/NT interface is crossed into the turbulent region. For instance, the enstrophy density, proportional to $Q_W$ , is zero in the irrotational flow region and high and more or less constant inside the turbulent region, after it undergoes a sharp jump near the T/NT interface. Inside the turbulent region, at a distance of only $1.7\eta$ from the T/NT interface, where $\eta$ is the Kolmogorov microscale, the invariants $Q_W$ and $Q_S$ suggest that large scale coherent vortices already exist in the flow. Furthermore, the joint probability density function of $Q$ and $R$ already displays its well known teardrop shape at that location. Moreover, the geometry of the straining (or deformation) of the fluid elements during the turbulent entrainment process is preferentially characterized by biaxial expansion with ${\alpha }_S:{\beta }_S:{\gamma }_S=2:1:-3$ , where ${\alpha }_S$ , ${\beta }_S$ , and ${\gamma }_S$ are the eigenvalues of the rate-of-strain tensor arranged in descending order. Based on an analysis of the invariants, many aspects of the flow topology inside the turbulent region at a distance of only $1.7\eta$ from the T/NT interface are already similar to those observed deep inside the turbulent region.

Detailed velocity measurements and numerical predictions are presented for the flow through a plane nominally two-dimensional duct with a Symmetric sudden expansion of area ratio 1:2. Both the experiments and the predictions confirm a symmetry-breaking bifurcation of the flow leading to one long and one short Separation zone for channel Reynolds numbers above 125, based on the upstream channel height and the maximum flow velocity upstream. With increasing Reynolds numbers above this value, the short separated region remains approximately constant in length whereas the long region increases in length.The experimental data were obtained using a one-component laser-Doppler anemometer at many Reynolds number values, with more extensive measurements being performed for the three Reynolds numbers 70, 300 and 610. Predictions were made using a finite volume method and an explicit quadratic Leith type of temporal discretization. In general, good agreement was found between measured and predicted velocity profiles for all Reynolds numbers investigated.

The characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$ , ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$ , and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$ , where ${u}_{0} $ , and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$ , tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$ , ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.