Related papers: A Weakly Nonlinear Analysis of Impulsively-Forced …
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…
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…
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…
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 use symmetry considerations to investigate how damped modes affect pattern selection in multi-frequency forced Faraday waves. We classify and tabulate the most important damped modes and determine how the corresponding resonant triad…
We report the quantitative experimental observation of the weak inertial-wave turbulence regime of rotating turbulence. We produce a statistically steady homogeneous turbulent flow that consists of nonlinearly interacting inertial waves,…
Motivated by the rich variety of complex patterns observed on the surface of fluid layers that are vibrated at multiple frequencies, we investigate the effect of such resonant forcing on systems undergoing a Hopf bifurcation to spatially…
The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different…
We present a theoretical analysis of phase separation in the presence of a spatially periodic forcing of wavenumber q traveling with a velocity v. By an analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model we find…
We analyze the effects of spatially extended periodic forcing on the dynamics of one-dimensional excitation waves. Entrainment of unstable primary waves has been studied numerically for different amplitudes and frequencies of additional…
During comprehensive study of weakly nonlinear interaction of surface capillary waves, processes of resonant and non-resonant interactions were considered both numerically and analytically: merging of two waves into one and waves on the…
We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…
We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…
Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a non-monotonic dispersion relation. The effect of a parametric driving on such waves is studied within suitable coupled Ginzburg-Landau equations. Due to the…
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 study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the…