Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: a hydrodynamic white hole.

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasize the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a "superluminal" dispersion relation, that is, that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible "trans-Planckian distortion" of black or white holes.

Pattern formation in bubbles emerging periodically from a liquid free surface.

Patterns formed by centimeter scale bubbles on the free surface of a viscous liquid are investigated in a cylindrical container. These bubbles emerge periodically at the surface and interact with each other in the central zone. Their radial emission, due to interaction and radial surface flow, leads to the formation of a variety of patterns. Different star-like and spiral patterns appear spontaneously by increasing the bubble emergence frequency. It is found that these patterns are due to a constant angular shift in the bubble emission direction. Measurements of this angular shift show a supercritical bifurcation accompanied by a transition from a pattern of two opposed straight arms to spiral patterns. By applying the tools and concepts from the study of leaf arrangement in botany (phyllotaxis), the recognized patterns and the mechanism of the pattern formation are discussed. Close similarities to the leaf arrangement are found in the behavior of the angular shift and the patterns. These findings suggest that the observed patterns are formed by a packing mechanism of successively appearing elements (bubbles), which is similar to that of the leaves at the earliest stage of phyllotaxis.

Structures of a continuously fed two-dimensional viscous film under a destabilizing gravitational force.

We study the gravity induced instability of a liquid film formed below a plane grid which is used as a porous media in an original hydrodynamic experiment. The film is continuously supplied with a controlled flow rate. We give through a phase diagram the full spectrum of the different flow regimes and we investigate the dynamics of the observed structures. True secondary instabilities of a 2D periodic pattern are described. The control parameters are the flow rate and the viscosity.