Self-similar impulsive capillary waves on a ligament

We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the dynamics, including surface tension and viscous effects. An exact self-similar solution to the linearized equations is successfully compared to experiments made with millimetric ligaments. Another non-linear self-similar solution of the full set of equations is found numerically. Both the linear and non-linear solutions show that the axial depth at which the liquid is affected by the motion of the cylinder scales like $\sqrt{t}$. The non-linear solution presents the peculiar feature that there exists a maximum driving velocity $U^\star$ above which the solution disappears, a phenomenon probably related to the de-pinning of the contact line observed in experiments for large pulling velocities

Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets

We study a liquid jet that breaks up into drops in an external co-flowing liquid inside a confining microfluidic geometry. The jet breakup can occur right after the nozzle in a phenomenon named dripping or through the generation of a liquid jet that breaks up a long distance from the nozzle, which is called jetting. Traditionally, these two regimes have been considered to reflect the existence of two kinds of spatiotemporal instabilities of a fluid jet, the dripping regime corresponding to an absolutely unstable jet and the jetting regime to a convectively unstable jet. Here, we present quantitative measurements of the dripping and jetting regimes, both in an unforced and a forced state, and compare these measurements with recent theoretical studies of spatiotemporal instability of a confined liquid jet in a co-flowing liquid. In the unforced state, the frequency of oscillation and breakup of the liquid jet is measured and compared to the theoretical predictions. The dominant frequency of the jet oscillations as a function of the inner flow rate agrees qualitatively with the theoretical predictions in the jetting regime but not in the dripping regime. In the forced state, achieved with periodic laser heating, the dripping regime is found to be insensitive to the perturbation and the frequency of drop formation remains unaltered. The jetting regime, on the contrary, amplifies the externally imposed frequency, which translates in the formation of drops at the frequency imposed by the external forcing. In conclusion, the dripping and jetting regimes are found to exhibit the main features of absolutely and convectively unstable flows respectively, but the frequency selection in the dripping regime is not ruled by the absolute frequency predicted by the stability analysis.Comment: 10 pages, 12 figures, to appear in Physics of Fluid

On the three-dimensional temporal spectrum of stretched vortices

The three-dimensional stability problem of a stretched stationary vortex is addressed in this letter. More specifically, we prove that the discrete part of the temporal spectrum is only associated with two-dimensional perturbations.Comment: 4 pages, RevTeX, submitted to PR

Experimental and theoretical study of the elliptic instability in a rotating stratified flow

The combined effects of Coriolis force and buoyancy effects on the dynamics of a weakly elliptical bounded vortex are treated theoretically as well as experimentally. As predicted theoretically, stratification and rotation have antagonist contributions to the stability of an elliptical vortex. Thus if the stratification is strong enough (Nb>Omega_c, Nb and Omega_c being respectively the Brunt-Väisälä frequency and the rotation rate of the flow in a frame rotating with the elliptical deformation at angular velocity Omega_t), we have observed that only anticyclones (such that |Wa|<Omega_c with Wa=2(Omega_c+Omega_t)) are unstable, whereas the cyclones are always stable. In addition if the stratification is weak, instability areas over change. These instability thresholds found theoretically have been observed experimentally with a good accuracy and the measured growth rate are in a good agreement with those predicted by a linear stability analysis in the limit of small deformation

Magnetic field induced by elliiptical instability in a rotating tidally distorded sphere

It is usually believed that the geo-dynamo of the Earth or more generally of other planets, is created by the convective fluid motions inside their molten cores. An alternative to this thermal or compositional convection can however be found in the inertial waves resonances generated by the eventual precession of these planets or by the possible tidal distorsions of their liquid cores. We will review in this paper some of our experimental works devoted to the elliptical instability and present some new results when the experimental fluid is a liquid metal. We show in particular that an imposed magnetic field is distorted by the spin- over mode generated by the elliptical instability. In our experiment, the field is weak (20 Gauss) and the Lorenz force is negligible compared to the inertial forces, therefore the magnetic field does not modify the fluid flow and the pure hydrodynamics growth rates of the instability are recovered through magnetic measurements

Three-dimensional instability during vortex merging

4 p.The interaction of two parallel vortices of equal circulation is observed experimentally. For low Reynolds numbers ($Re$), the vortices remain two-dimensional and merge into a single one, when their time-dependent core size exceeds approximately 30\% of the vortex separation distance. At higher $Re$, a three-dimensional instability is discovered, showing the characteristics of an elliptic instability of the vortex cores. The instability rapidly generates small-scale turbulent motion, which initiates merging for smaller core sizes and produces a bigger final vortex than for laminar 2D flow