skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Grid states and nonlinear selection in parametrically excited surface waves

Abstract

Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond to 'grid' states. Grid states are superlattices in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly stable modes. Specific driving phase combinations govern the selection of different grid states.

Authors:
;  [1]
  1. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
Publication Date:
OSTI Identifier:
21069768
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.73.055302; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUIDS; INTERACTIONS; NONLINEAR PROBLEMS; SUPERLATTICES; VECTORS; WAVE PROPAGATION

Citation Formats

Epstein, T., and Fineberg, J. Grid states and nonlinear selection in parametrically excited surface waves. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.055302.
Epstein, T., & Fineberg, J. Grid states and nonlinear selection in parametrically excited surface waves. United States. doi:10.1103/PHYSREVE.73.055302.
Epstein, T., and Fineberg, J. Mon . "Grid states and nonlinear selection in parametrically excited surface waves". United States. doi:10.1103/PHYSREVE.73.055302.
@article{osti_21069768,
title = {Grid states and nonlinear selection in parametrically excited surface waves},
author = {Epstein, T. and Fineberg, J.},
abstractNote = {Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond to 'grid' states. Grid states are superlattices in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly stable modes. Specific driving phase combinations govern the selection of different grid states.},
doi = {10.1103/PHYSREVE.73.055302},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 5,
volume = 73,
place = {United States},
year = {Mon May 15 00:00:00 EDT 2006},
month = {Mon May 15 00:00:00 EDT 2006}
}
  • In experiments with parametrically excited capillary waves on the surface of a liquid with random pumping it was found that the transition to an irregular wave field starts to occur at a low supercriticality. Pulsations in the intensity of the ripples with almost complete preservation of the wave-field structure were noticed. The characteristic frequency of the pulsations calculated from experimental samples turned out to depend on the supercriticality. The results of numerical modeling were in good agreement with experiment.
  • The authors present results of numerical simulations of coupled one-dimensional Ginzburg-Landau equations that describe parametrically excited waves. They focus on a new regime in which the Eckhaus sideband instability does not lead to an overall change in the wavelength via the occurrence of a single phase slip but instead leads to double phase slips. They are characterized by the phase slips occurring in sequential pairs, with the second phase slip quickly following and negating the first. The resulting dynamics range transient excursions from a fixed point resembling those seen in excitable media, to periodic solutions of varying complexity and chaoticmore » solutions. In larger systems they find in addition localized spatiotemporal chaos, where the solution consists of a chaotic region with quiescent regions on each side. They explain the localization using an effective phase diffusion equation which can be viewed as arising from a homogenization of the chaotic state.« less
  • A direct perturbation analysis of solitary waves for a parametric Ginzburg Landau equation describing parametric excitation of waves in nonlinear dispersive and dissipative systems is presented. The method is used to study the influence on soliton dynamics of various perturbations, including external fields, stochastic driving forces, higher-order effects, and soliton interactions. A remarkable and quite general result of the analysis is that when the system is dissipative the dynamical motion induced by the perturbation is counteracted by the dissipative term, making dissipative solitary waves less sensitive to perturbations than solitons in the conservative case. {copyright} {ital 1997} {ital The Americanmore » Physical Society}« less