Figure 1

Theoretical vortex model. The $z$ axis is directed along the vortex axis and $z=0$ defines the center of the channel and the stagnation point. $\gamma (r,z)$ denotes the axial stretching and $\beta \equiv {\partial }_z{V}_z(r=\infty ,z=0)>0$ the external stretching at $z=0$.Reuse & Permissions

Figure 2

Sketch of the experimental water channel. Vorticity is generated in a boundary layer which is developing over a flat plate due to the presence of a constant flow $U$. Such a boundary layer is then separated behind an obstacle. At the very same location, the input mass flux is entirely sucked into two tubes, each one originating from each lateral wall. Both mechanisms induce the roll-up of vorticity into a vortex structure (whose axis is along the $z$ coordinate as in Fig. 1). A dye visualization is displayed in the inserted box.Reuse & Permissions

Figure 3

In plain lines, $V_{\theta }$ profiles [averaged particle image velocimetry (PIV) measurements] for nondimensional $z=0$, 0.17, 0.3, 0.5 ($L=6\mathrm{c}\mathrm{m}$, imposed by the channel width) and $z=0.7$ ($L=3\mathrm{c}\mathrm{m}$ when reducing the channel width). In dotted lines, corresponding theoretical solutions $V_{\theta }(r,z)=V_{\theta }^{(0)}(r)+V_{\theta }^{(2)}(r)z^2$ ($B=1.6$ for $L=3\mathrm{c}\mathrm{m}$ and $B=11.5$ for $L=6\mathrm{c}\mathrm{m}$).Reuse & Permissions

Figure 4

(a) $V_z(r,z)$ field (instantaneous PIV measurement) for $L=3\mathrm{c}\mathrm{m}$. (b) Fit of the previous field in ${\gamma }_{\mathrm{e}\mathrm{x}\mathrm{p}}^{(0)}(r)z+{\gamma }_{\mathrm{e}\mathrm{x}\mathrm{p}}^{(2)}(r)z^3/3$ performed at each $r$. (c) Theoretical field $V_z(r,z)={\gamma }^{(0)}(r)z+{\gamma }^{(2)}(r)z^3/3$. (d) Comparison between ${\gamma }_{\mathrm{e}\mathrm{x}\mathrm{p}}^{(0)}(r)$ and ${\gamma }^{(0)}(r)$ [${\gamma }_{\mathrm{e}\mathrm{x}\mathrm{p}}^{(2)}(r)$, being of the same order of the noise, is not displayed].Reuse & Permissions