Liquid jet eruption from hollow relaxation

A cavity hollowed out on a free liquid surface is relaxing, forming an intense liquid jet. Using a model experiment where a short air pulse sculpts an initial large crater, we depict the different stages in the gravitational cavity collapse and in the jet formation. Prior eversion, all cavity profiles are found to exhibit a shape similarity. Following hollow relaxation, a universal scaling law establishing an unexpected relation between the jet eruption velocity, the initial cavity geometry and the liquid viscosity is evidenced experimentally. On further analysing the jet forms we demonstrate that the stretched liquid jet also presents shape similarity. Considering that the jet shape is a signature of the initial flow focusing, we elaborate a simple model capturing the key features of the erupting jet velocity scaling

A pressure impulse theory for hemispherical liquid impact problems

Liquid impact problems for hemispherical fluid domain are considered. By using the concept of pressure impulse we show that the solution of the flow induced by the impact is reduced to the derivation of Laplace's equation in spherical coordinates with Dirichlet and Neumann boundary conditions. The structure of the flow at the impact moment is deduced from the spherical harmonics representation of the solution. In particular we show that the slip velocity has a logarithmic singularity at the contact line. The theoretical predictions are in very good agreement both qualitatively and quantitatively with the first time step of a numerical simulation with a Navier-Stokes solver named Gerris.Comment: 11 pages, 14 figures, Accepted for publication in European Journal of Mechanics - B/Fluid

Soft beams: when capillarity induces axial compression

We study the interaction of an elastic beam with a liquid drop in the case where bending and extensional effects are both present. We use a variational approach to derive equilibrium equations and constitutive relation for the beam. This relation is shown to include a term due to surface energy in addition of the classical Young's modulus term, leading to a modification of Hooke's law. At the triple point where solid, liquid, and vapor phases meet we find that the external force applied on the beam is parallel to the liquid-vapor interface. Moreover, in the case where solid-vapor and solid-liquid interface energies do not depend on the extension state of the beam, we show that the extension in the beam is continuous at the triple point and that the wetting angle satisfy the classical Young-Dupr\'e relation

On the physics of fizzing: How bubble bursting controls droplets ejection

Bubbles at a free surface surface usually burst in ejecting myriads of droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we propose a simple scaling for the jet velocity and we unravel experimentally the intricate roles of bubble shape, capillary waves, gravity and liquid properties. We demonstrate that droplets ejection unexpectedly changes with liquid properties. In particular, using damping action of viscosity, self-similar collapse can be sheltered from capillary ripples and continue closer to the singular limit, therefore producing faster and smaller droplets.These results pave the road to the control of the bursting bubble aerosols

Transient energy growth for the Lamb-Oseen vortex

The transient evolution of infinitesimal flow disturbances whichoptimally induce algebraic growth in the Lamb-Oseen (gaussian) vortex is studied using a direct-adjoint technique. This optimal perturbation analysis reveals that the Lamb-Oseen vortex allows for intense amplification of kinetic energy for 2D and 3D perturbations of azimuthal wavenumber $m = 1$. In both cases, the disturbances experiencing the most growth initially take the form of concentrated spirals at the outer periphery of the vortex which rapidly excite bending waves within the vortex core. In the limit of large wavelengths, the optimal perturbation leads to arbitrary large growths via an original scenario combining the Orr mechanism with vortex induction

On vortex rings around vortices: an optimal mechanism

Stable columnar vortices subject to hydrodynamic noise (\eg turbulence) present some recurrent behaviours like the systematic development of vortex rings at the periphery of the vortex core. This phenomenon still lacks a comprehensive explanation, partly because it is not associated to an instability \textit{stricto sensu}. The aim of the present paper is to identify the physical mechanism triggering this intrinsic feature of vortices using an optimal perturbation analysis as a tool of investigation. We found that the generation of vortex rings is linked to the intense and rapid amplification of specific disturbances in the form of azimuthal velocity streaks that eventually evolve into azimuthal vorticity rolls generated by the rotational part of the local Coriolis force. This evolution thus appears to follow a scenario opposite to the classical lift-up view, where rolls give rise to streaks