منابع مشابه
Pattern Selection in Faraday Waves
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 equation that is of gradient form. The associated Lyapunov function is calculated for different regular patterns to determine the selected pattern near threshold as a function o...
متن کاملAmplitude equations and pattern selection in Faraday waves
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 equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are com...
متن کاملPattern Selection for Faraday Waves in an Incompressible Viscous Fluid
Abstract. When a layer of fluid is oscillated up and down with a sufficiently large amplitude patterns form on the surface: a phenomenon first observed by Faraday. A wide variety of such patterns have been observed from regular squares and hexagons to superlattice and quasipatterns and more exotic patterns such as oscillons. Previous work has investigated the mechanisms of pattern selection usi...
متن کاملAmplitude equation and pattern selection in Faraday waves.
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 equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are com...
متن کاملTwo–Frequency Forced Faraday Waves: Weakly Damped Modes and Pattern Selection
Recent experiments [1] 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 onset simultaneously, but with different spatial wavenumbers. The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 1997
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.79.2670