Related papers: A Simple Model for Faraday Waves
The propagation of wave disturbances over a vertically oscillating liquid may form standing waves, known as Faraday waves. Here we present an alternative description of the generation and evolution of Faraday waves by nonlinear resonant…
The standing surface waves in a rectangular vertically oscillating vessel filled with water (Faraday waves) in the presence of a floating elastic sheet are studied experimentally and theoretically. The threshold amplitude of the instability…
Vertical oscillation of a fluid interface above a critical amplitude excites the Faraday instability, typically manifesting itself as a standing wave pattern. Fundamentally, the phenomenon is an example of parametric resonance. At high…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
We present an analytical stability theory for the onset of the Faraday instability, applying over a wide frequency range between shallow water gravity and deep water capillary waves. For sufficiently thin fluid layers the surface is…
We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
A weakly nonlinear model for two-dimensional Faraday waves over infinite depth is derived and studied. Sideband instability of monochromatic standing waves as well as non-monochromatic solutions are studied analytically. Persistent…
A phenomenological model of parametric surface waves (Faraday waves) is introduced in the limit of small viscous dissipation that accounts for the coupling between surface motion and slowly varying streaming and large scale flows (mean…
We present a systematic nonlinear theory of pattern selection for parametric surface waves (Faraday waves), not restricted to fluids of low viscosity. A standing wave amplitude equation is derived from the Navier-Stokes equations that is of…
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…
Faraday waves are generated at the air/liquid interface inside an array of square cells. As the free surface inside each cell is destabilizing due to the oscillations, the shape of the free surface is drastically changing. Depending on the…
In this paper, the closed-form analytic solutions of two new Faraday's standing solitary waves due to the parametric resonance of liquid in a vessel vibrating vertically with a constant frequency are given for the first time. Using a model…
We report on an experimental study of the Faraday instability in a vibrated fluid layer situated over a permeable and rough substrate, consisting either of a flat solid plate or of woven meshes having different openings and wire diameters,…
Waves patterns in the Faraday instability have been studied for decades. Besides the rich dynamics that can be observed on the waves at the interface, Faraday waves hide beneath them an elusive range of flow patterns --or streaming…
We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a…
Metamaterials enable the emergence of novel physical properties due to the existence of an underlying sub-wavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern…
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude…
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
We measure the velocities of the mean flows which are driven by curved rolls in a pattern formation system. Curved rolls in Faraday waves are generated in experimental cells consisting of channels with varying widths. The mean flow…