Related papers: Amplitude equations and pattern selection in Farad…
We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle waveform rather than by a sine wave. The calculation is simple…
We consider the stability of periodic gravity-capillary waves of finite amplitude for small values of the surface tension. Linear stability with respect to both superharmonic and subharmonic perturbations is calculated for each solution,…
A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the…
We report on the generation of an intermittent wave field driven by a horizontally moving wave maker interacting with Faraday waves. The spectrum of the local gravitocapillary surface wave fluctuations displays a power law in frequency for…
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for…
A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the…
We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single and multi-frequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…
We present measurements on parametrically driven surface waves (Faraday waves) performed in the vicinity of a bi-critical point in parameter space, where modes with harmonic and subharmonic time dependence interact. The primary patterns are…
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…
We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external…
Surface waves on a liquid air interface excited by a vertical vibration of a fluid layer (Faraday waves) are employed to investigate the phase relaxation of ideally ordered patterns. By means of a combined frequency-amplitude modulation of…
The linear instability of Faraday waves in Hele-Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of…
We prove the existence of small steady periodic capillary-gravity water waves for general stratified flows, where we allow for stagnation points in the flow. We establish the existence of both laminar and non-laminar flow solutions for the…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
This technical note is a complement to an earlier paper [Benzoni-Gavage \& Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a basic model for propagating phase boundaries that was proved to admit surface waves…
Evolution of a Langmuir wave is studied numerically for finite amplitudes slightly above the threshold which separates damping from nondamping cases. Arrest of linear damping is found to be a second-order effect due to ballistic evolution…
Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to…
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. We consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic…