Related papers: Rhombic Patterns Near a Bicritical Point in Period…
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…
Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio…
Many of the interesting patterns seen in recent multi-frequency Faraday experiments can be understood on the basis of three-wave interactions (resonant triads). In this paper we consider two-frequency forcing and focus on a resonant triad…
Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency parametrically excited surface waves exhibit an intriguing "superlattice" wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves…
A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability…
We examine three experimental observations of Faraday waves generated by two-frequency forcing, in which a primary hexagonal pattern becomes unstable to three different superlattice patterns. We use the symmetry-based approach developed by…
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 recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales [1]. These patterns both arise as secondary states once the primary…
A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating…
We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the…
Pattern forming with externally imposed symmetry is ubiquitous in nature but lightly studied.We present experimental studies of pattern formation and selection by spatial periodic forcing in rapidly rotating convection. We observe symmetric…
We report on surface wave pattern formation in a Faraday experiment operated at a very shallow filling level, where modes with a subharmonic and harmonic time dependence interact. Associated with this distinct temporal behavior are…
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…
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…
We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As…
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited…
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…
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…
Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits…
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…