Broken-parity waves at a driven fluid-air interface

Pattern dynamics in a perturbed printer's instability experiment

We report experimental results concerning observation of a pattern forming system, subject to directional viscous fingering (printer's instability). This system was excited by a time-dependent, periodic perturbation. A variety of spatiotemporal effects was observed, including pattern transient dynamics, wave vector selection, and morphological transitions. Detailed measurement of pattern shape and its associated Fourier modes assured the detection of a crossover between different regimes of the pattern evolution.

Stabilized Kuramoto-Sivashinsky equation: a useful model for secondary instabilities and related dynamics of experimental one-dimensional cellular flows

We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of secondary instabilities or transition toward disorder. We compare some of these collective behaviors to those observed in experiments. In particular, destabilization scenarios of bifurcated states are studied in a spatially semi-extended situation, which is common in realistic patterns, but has been barely explored so far.

Propagating wave pattern on a falling liquid curtain

A regular pattern of surface waves is observed on a liquid curtain falling from a horizontal, wetted tube, maintained between two vertical wires. Since the upper boundary is not constrained in the transverse direction, the top of the curtain enters a pendulum-like motion, when the flow rate is progressively reduced, coupled to the propagation of curtain undulations, structured as a checkerboard. This structure is formed by two patterns of propagating waves. In some sense, these propagating patterns replace the stationary pattern of liquid columns observed at a lower flow rate. Measurements of phase velocity, frequency, and wavelength are reported. The data are in agreement with a simple dimensional argument suggesting that the wave velocity is proportional to the surface tension divided by the mass flux of liquid per unit length. This scaling is also that followed by the fluid velocity at the so-called transonic point, i.e., the point where the fluid velocity equals that of sinuous waves. We finally discuss the implications of these results for the global stability of liquid curtains.