Parametric excitation of multimode dissipative systems

Interplay between Turing mechanisms can increase pattern diversity

We use the context of dryland vegetation to study a general problem of complex pattern-forming systems: multiple pattern-forming instabilities that are driven by distinct mechanisms but share the same spectral properties. We find that the co-occurrence of two Turing instabilities when the driving mechanisms counteract each other in some region of the parameter space results in the growth of a single mode rather than two interacting modes. The interplay between the two mechanisms compensates for the simpler dynamics of a single mode by inducing a wider variety of patterns, which implies higher biodiversity in dryland ecosystems.

Observation of star-shaped surface gravity waves

We report a new type of standing gravity wave of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vertically vibrating a tank. The symmetry of the star (i.e., the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. We show that a nonlinear resonant coupling between three gravity waves can be envisaged to trigger the observed symmetry breaking, although more complex interactions certainly take place in the final periodic state.

New standing solitary waves in water

By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are, respectively, of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency. The two-dimensional even pattern presents a certain similarity in the shape with the 3D axisymmetric oscillon originally recognized at the surface of a vertically vibrated layer of brass beads. The stable, 2D odd standing wave has never been observed before in any media.

Onset condition of modulated Rayleigh-Bénard convection at low frequency

The onset condition of convection in a layer of fluid bounded by isothermal walls, with lower temperature varying sinusoidally in time at very low nondimensional modulation frequency, is derived in closed form, based on the Floquet theory and using a matched-asymptotic WKB method.