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In this Brief Communication we study experimentally the flow regimes that appear in co-axial air-water jets discharging into a stagnant air atmosphere and we propose a simple explanation for their occurrence based on linear, local, spatiotemporal stability theory. In addition to the existence of a periodic bubbling regime for low enough values of the water-to-air velocity ratio, $u=u_w/u_a$, our experiments revealed the presence of a jetting regime for velocity ratios higher than a critical one, $u_c$. In the bubbling regime, bubbles form periodically from the tip of an air ligament whose length increases with $u$. However, when $u> u_c$ a long, slender gas jet is observed inside the core of the liquid coflow. Since in the jetting regime the downstream variation of the flow field is slow, we performed a local, linear spatiotemporal stability analysis with uniform velocity profiles to model the flow field of the air-water jet. Similar to the transition from dripping to jetting in capillary liquid jets, the analysis shows that the change from the bubbling to the jetting regime can be understood in terms of the transition from an absolute to a convective instability., Comment: 6 pages, 3 figures

We report a detailed experimental characterization of the periodic bubbling regimes that take place in an axisymmetric air-water jet when the inner air stream is forced by periodic modulations of the pressure at the upstream air feeding chamber. When the forcing pressure amplitude is larger than a certain critical value, the bubble formation process is effectively driven by the selected frequency, leading to the formation of nearly monodisperse bubbles whose volume is reduced by increasing the forcing frequency. We reveal the existence of two different breakup modes, M1 and M2, under effective forcing conditions. The bubble formation in mode M1 resembles the natural bubbling process, featuring an initial radial expansion of an air ligament attached to the injector, whose initial length is smaller than the wavelength of a small interfacial perturbation induced by the oscillating air flow rate. The expansion stage is followed by a ligament collapse stage, which begins with the formation of an incipient neck that propagates downstream while collapsing radially inwards, leading to the pinch-off of a new bubble. These two stages take place faster than in the unforced case as a consequence of the the air flow modulation induced by the forcing system. The breakup mode M2 takes place with an intact ligament longer than one disturbance wavelength, whereby the interface already presents a local necking region at pinch-off, and leads to the formation of bubbles from the tip of an elongated air filament without an expansion stage. Scaling laws that provide closed expressions for the bubble volume, the intact ligament length, and the transition from the M1 breakup mode to the M2, as functions of the relevant governing parameters, are deduced from the experimental data., Comment: 27 pages, 12 figures, submitted to Int. J. Multiphase Flow

We analyze the global linear stability of the axisymmetric flow around a spinning bullet-shaped body as a function of the Reynolds number, $Re=w_{\infty}D/\nu$, and of the rotation parameter $\Omega=\omega D/(2 w_{\infty})$, in the ranges $Re<450$ and $0\leq\Omega\leq 1$. Here, $w_{\infty}$ and $\omega$ are the free-stream and the body rotation velocities respectively, and $\nu$ is the fluid kinematic viscosity. The spectrum and the eigenfunctions obtained allow us to explain the different bifurcations from the axisymmetric state observed in previous numerical studies. Our results reveal that three global eigenmodes, denoted Low-Frequency (LF), Medium-Frequency (MF) and High-Frequency (HF) modes, become unstable in different regions of the $Re-\Omega$ parameter plane. We provide precise computations of the corresponding neutral curves, that divide the $Re-\Omega$ plane into four different regions: the stable axisymmetric flow prevails for small enough values of $Re$ and $\Omega$, while three different frozen states, where the wake structures co-rotate with the body at different angular velocities, take place as a consequence of the destabilization of the LF, MF and HF modes. Several direct numerical simulations of the nonlinear state associated to the MF mode, identified here for the first time, are also reported to complement the linear stability results. Finally, we point out the important fact that, since the axisymmetric base flow is $SO(2)$-symmetric, the theory of equivariant bifurcations implies that the weakly non-linear regimes that emerge close to criticality must necessarily take the form of rotating-wave states. These states, previously referred to as frozen wakes in the literature, are thus shown to result from the base-flow symmetry., Comment: 25 pages, 16 figures, 5 tables. Accepted for publication in J. Fluid Mech