Related papers: A Simple Model for Faraday Waves
The Faraday problem is an important pattern-forming system that provides some middle ground between systems where the initial instability involves just a single mode and in which complexity then results from mode interactions or secondary…
Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show low-frequency modulations corresponding to the…
The solution was found from Navier-Stokes equation and boundary conditions with interfacial tension as function of the film substance concentration. Here the method of Chen&Vinals is used. It was found that adding to coefficient leads to…
We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.
To understand the process of pattern formation in a low-density granular flow, we propose a simple particle model. This model considers spherical particles moving over an inclined flat surface based on three forces: gravity as the driving…
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 walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave-particle features formerly thought to be exclusive…
The instability of the interface between a dielectric and a conducting liquid, excited by a spatially homogeneous interface-normal time-periodic electric field, is studied based on experiments and theory. Special attention is paid to the…
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…
In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologies for future…
In this paper, we study the structure and stability of line driven winds using numerical hydrodynamic simulations. We calculate the radiation force from an explicit non-local solution of the radiation transfer equation, rather than a…
In nature turbulent flows exist that are neither simply 2D nor 3D but boundary conditions, such as varying stratification, force them towards the one or the other. Here, we report the first evidence of the co-existence of 2D and 3D…
The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
In a magnetic fluid parametrically driven surface waves can be excited by an external oscillating magnetic field. A static magnetic field changes the restoring forces and damping coefficients of the various surface waves. This property…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…
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…
It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequencies. The amplitude is not required to be small (apart…
Through experimentation, we have discovered that with the changing of driving conditions, the Faraday waves undergo two abrupt transitions in spatiotemporal order: onset and instability. The driving amplitudes and frequencies corresponding…