Wakes are medium perturbations created by a moving object, such as wave patterns behind boats, or wingtip vortices following an aircraft. Here, we report about an experimental study of an uncharted ...form of parabolic wakes occurring in media with the group velocity twice larger than the phase velocity, as opposed to the conventional case of Kelvin wakes. They are formed by moving a laser spot on a thin plate, which excites a unique wake pattern made of confocal parabolas, due to the quadratic dispersion of the zero-order flexural Lamb mode. If the spatial dimensions are rescaled by the perturbation velocity and material constant, we obtain a single universal wake with constant parabolic focal lengths. We demonstrate an evanescent regime above the critical frequency where the wave components oscillate exclusively in the direction parallel to the perturbation path, with an opening angle of 90 ∘ . We define a dimensionless number, analogous to Froude and Mach numbers, which determines whether or not the complete parabolic wake pattern will be excited by the moving source. Finally, we generalize the physics of wake shapes to arbitrary dispersion relations. Published by the American Physical Society 2024
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what ...happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable states, the oscillator will be perturbed by the defect and finally reach another stable state, which can be its initial one or the other one. For some critical value of the defect parameter, the final state changes abruptly. We theoretically and experimentally investigate such transition both in the linear and nonlinear cases, and the effect of nonlinearities is discussed. A topological interpretation in terms of winding number is proposed, and we show that winding changes correspond to singularities in the temporal dynamics. An experimental observation of such transition is performed using parametric Faraday instability at the surface of a vibrated fluid.Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable states, the oscillator will be perturbed by the defect and finally reach another stable state, which can be its initial one or the other one. For some critical value of the defect parameter, the final state changes abruptly. We theoretically and experimentally investigate such transition both in the linear and nonlinear cases, and the effect of nonlinearities is discussed. A topological interpretation in terms of winding number is proposed, and we show that winding changes correspond to singularities in the temporal dynamics. An experimental observation of such transition is performed using parametric Faraday instability at the surface of a vibrated fluid.
When placed over a less dense medium, a liquid layer will typically collapse downwards if it exceeds a certain size, as gravity acting on the lower liquid interface triggers a destabilizing effect ...called a Rayleigh-Taylor instability
. Of the many methods that have been developed to prevent the liquid from falling
, vertical shaking has proved to be efficient and has therefore been studied in detail
. Stabilization is the result of the dynamical averaging effect of the oscillating effective gravity. Vibrations of liquids also induce other paradoxical phenomena such as the sinking of air bubbles
or the stabilization of heavy objects in columns of fluid at unexpected heights
. Here we take advantage of the excitation resonance of the supporting air layer to perform experiments with large levitating liquid layers of up to half a litre in volume and up to 20 centimetres in width. Moreover, we predict theoretically and show experimentally that vertical shaking also creates stable buoyancy positions on the lower interface of the liquid, which behave as though the gravitational force were inverted. Bodies can thus float upside down on the lower interface of levitating liquid layers. We use our model to predict the minimum excitation needed to withstand falling of such an inverted floater, which depends on its mass. Experimental observations confirm the possibility of selective falling of heavy bodies. Our findings invite us to rethink all interfacial phenomena in this exotic and counter-intuitive stable configuration.
Here, we study and implement the temporal analog in time disordered sytems. A spatially homogeneous medium is endowed with a time structure composed of randomly distributed temporal interfaces. This ...is achieved through electrostriction between water surface and an electrode. The wave field observed is the result of the interferences between reflected and refracted waves on the interfaces. Although no eigenmode can be associated with the wave field, several common features between space and time emerge. The waves grow exponentially depending on the disorder level in agreement with a 2D matrix evolution model such as in the spatial case. The relative position of the momentum gap appearing in the time modulated systems plays a central role in the wave field evolution. When tuning the excitation to compensate for the damping, transient waves, localized in time, appear on the liquid surface. They result from a particular history of the multiple interferences produced by a specific sequence of time boundaries.
The control of wave propagation based on refraction principles offers unparalleled possibilities as shown by the striking example of optics. This approach is unfortunately limited for water waves as ...it relies mainly on variations of the liquid depth which, while controlling the wave velocity, also trigger nonlinearities and damping. In this article, we show experimentally that electrostriction allows to implement extensive refraction-based control of water waves in a precise and contactless manner. The setup consists of an electrode under high voltage placed above the grounded conductive water. The waves propagating under the electrode can be slowed down up to approximately half their speed compared to free propagation. We characterize the Snell-Descartes laws of refraction and the total internal reflection for the water waves. We implement emblematic refraction-based devices such as electrically tunable focusing lenses, waveguides without obstacles, and beam splitters based on frustrated internal reflection to perform interference experiments.
Wave localization induced by spatial disorder is ubiquitous in physics. Here, we study the temporal analog of such phenomenon on water waves. Our time disordered media consists in a collection of ...temporal interfaces achieved through electrostriction between water surface and an electrode. The wave field observed is the result of the interferences between reflected and refracted waves on the interfaces. Although no eigenmode can be associated to the wave field, several common features between space and time emerge. The waves grow exponentially depending on the noise level in agreement with a 2D matrix evolution model such as in the spatial case. The relative position of the momentum-gap appearing in the time modulated systems plays a central role in the wave field evolution. When tuning the excitation to compensate for the damping, transient waves, localized in time, appear on the liquid surface. They result from a particular history of the multiples interferences produced by a specific sequence of time boundaries.
Gravity shapes liquids and plays a crucial role in their internal balance. Creating new equilibrium configurations irrespective of the presence of a gravitational field is challenging with ...applications on Earth as well as in zero-gravity environments. Vibrations are known to alter the shape of liquid interfaces and also to change internal dynamics and stability in depth. Here, we show that vibrations can also create an "artificial gravity" in any direction. We demonstrate that a liquid can maintain an inclined interface when shaken in an arbitrary direction. A necessary condition for the equilibrium to occur is the existence of a velocity gradient determined by dynamical boundary conditions. However, the no-slip boundary condition and incompressibility can perturb the required velocity profile, leading to a destabilization of the equilibrium. We show that liquid layers provide a solution, and liquid walls of several centimeters in height can thus be stabilized. We show that the buoyancy equilibrium is not affected by the forcing.
Vibrations can dynamically stabilize otherwise unstable liquid interfaces and produce new dynamic equilibria, called vibroequilibria. Typically, the vibrations are homogeneous in the liquid and the ...liquid interface remains approximately flat. Here, we produce controlled vertical vibration gradients by taking advantage of the resonant oscillations of sinking submerged bubbles. The locally increased amplitude of the vibrations induces a local elevation of the liquid interface that can be controlled and engineered. The mean elevation of the interface can be linked theoretically with the local vibration amplitude by a simple formula that is tested experimentally. In addition, the transport of a floating body at the interface can be induced by secondary flows triggered by the amplitude gradients of the liquid vibrations.
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