Perfect Resonant Absorption of Guided Water Waves by Autler-Townes Splitting.

The control of guided water wave propagation based on the Autler-Townes splitting resonance concept is demonstrated experimentally, numerically, and theoretically. Complete wave absorption is achieved using an asymmetric pointlike scatterer made of two closely spaced resonant side channels connected to a guide and designed so that its energy leakage is in perfect balance with the inherent viscous losses in the system. We demonstrate that the nature of the resonators and guide junction completely controls the positions of the wave numbers at the reflection and transmission zeros on the real axis; the asymmetry of the resonators completely controls their positions on the imaginary axis. Thus, by adjusting these two independent parameters, we obtain a zero reflection and transmission.

Experimental realization of a water-wave metamaterial shifter.

We demonstrate by quantitative experimental measurements that metamaterials with anisotropic properties can be used in the context of water waves to produce a reflectionless bent waveguide. The anisotropic medium consists in a bathymetry with subwavelength layered structure that shifts the wave in the direction of the waveguide bending (10°, 20°, and 30°). The waveguide filled with such metamaterial is tested experimentally and compared to a reference empty bent waveguide. The experimental method used to characterize the wave field allows for space-time resolved measurements of water elevation. Results show the efficiency of the shifter. Modal treatment of the experimental data confirms that the metamaterial prevents higher modes from being excited in the waveguide.

Time reversal of water waves.

We present time reversal experiments demonstrating refocusing of gravity-capillary waves in a water tank cavity. Owing to the reverberating effect of the cavity, only a few channels are sufficient to reconstruct the surface wave at the point source, even if the absorption is not negligible. Space-time-resolved measurements of the waves during the refocusing allow us to quantitatively demonstrate that the quality of the refocusing increases linearly with the number of reemitting channels. Numerical simulations corresponding to water waves at larger scales, with negligible damping, indicate the possibility of very high quality refocusing.

Different regimes for water wave turbulence.

We present an experimental study on gravity capillary wave turbulence in water. By using space-time resolved Fourier transform profilometry, the behavior of the wave energy density |η(k,ω)|(2) in the 3D (k,ω) space is inspected for various forcing frequency bandwidths and forcing amplitudes. Depending on the bandwidth, the gravity spectral slope is found to be either forcing dependent, as classically observed in laboratory experiments, or forcing independent. In the latter case, the wave spectrum is consistent with the Zakharov-Filonenko cascade predicted within wave turbulence theory.

Bubble splitting in oscillatory flows on ground and in reduced gravity.

The stability of centimeter scale air bubbles is studied in quiescent suspending liquid under an imposed oscillatory acceleration field. Experiments were performed in reduced- and normal-gravity environments. A strong acceleration resulted in an instability leading to the breakups of the bubbles in both gravity environments. The breakup onset was investigated and found to be characterized by a critical acceleration a (cr). The influence of the liquid viscosity and the gravitational environment was studied. Empirical correlations for the onset are presented and discussed with the intention to reveal splitting mechanism. The inertial mechanism often deemed to cause the breakup of drops subjected to a rapid gas stream is shown to give explanations consistent with the experiments. A breakup criterion for both gravitational environments is proposed through discussions from an energetic point of view.

Air bubbles under vertical vibrations.

This paper reports on an experimental study of the splitting instability of an air bubble a few centimetres in diameter placed in a sealed cylindrical cell filled with liquid and submitted to vertical oscillations. The response of the bubble to the oscillations is observed with a high-speed video camera. It is found that the bubble dynamics is closely associated with the acceleration of the cell Gamma. For small acceleration values, the bubble undergoes minor shape deformations. With increasing acceleration values, these deformations are amplified and for sufficiently large Gamma the bubble becomes toroidal. The bubble may then become unstable and split into smaller parts. The onset of bubble division is studied and its dependency on physical parameters such as the fluid viscosity, the fluid surface tension and the initial size of the bubble is presented. It is found that the criterion for the bubble splitting process is associated with a threshold based on the acceleration of the oscillations. Above this threshold, the number of bubbles present in the cell is observed to grow until a final steady state is reached. Data analysis reveals that the final bubble size may be characterized in terms of Bond number.

A nonuniformly stretched vortex.

A stretched vortex model is proposed which includes a nonuniform stretching in the radial direction that is clearly present in real flows, as well as a slow variation of velocity profiles along the vortex axis. Both features of this boundary layer approximation depart from the classical Burgers solution. This model is shown to be in very good agreement with experimental velocity measurements.

Scattering of sound by a vorticity filament: an experimental and numerical investigation.

A vorticity filament is investigated experimentally using the transmission of an ultrasonic wave through the flow. The analysis of the wave-front distortion provides noninvasive measurements of the vortex circulation and size. The latter is estimated by analytical calculations of the scattering of a plane wave by a vorticity filament. The case of a cylindrical wave incident on a vortex leads to similar experimental results which are successfully compared to a parabolic equation simulation. Finally, a finite-difference code based on linear acoustics is presented, in order to investigate the structure of the scattered wave numerically.

Farey sequences of spatiotemporal patterns in video feedback.

In this paper we present an experimental and theoretical description of the dynamic of spatial patterns obtained in a video feedback loop. A video camera monitors the screen to which it is connected and can turn around its optical axis at an angle alpha. Under certain conditions of brightness and magnification, this optoelectronic system produces spatiotemporal patterns in the form of spots located on a circle on the screen. These patterns are very similar to the spatial transverse modes obtained in other optical devices such as lasers or photorefractive media. It is possible to generate stationary patterns of n-fold symmetries for angles alpha=2pi/n. When the angle alpha varies around 2pi/n, the pattern rotates with a certain frequency proportional to the difference between 2pi/n and alpha. We discover more general patterns at angles 2pi/(p/k) with p-fold symmetry, following the hierarchy of the Farey algorithm which theoretically can produce stationary patterns at any angle alpha. Very accurate experiments were performed to observe these patterns up to the level k=6. This is the first time a Farey tree has been observed as a sequence of spatial patterns to our knowledge. Previous observations of this hierarchy were made only in the temporal domain.