Square patterns and secondary instabilities in driven capillary waves

Research output: Contribution to journalArticle

123 Citations (Scopus)

Abstract

Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from travelling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.

Original languageEnglish (US)
Pages (from-to)81-100
Number of pages20
JournalJournal of Fluid Mechanics
Volume225
DOIs
StatePublished - Jan 1 1991

Fingerprint

capillary waves
Amplitude modulation
standing waves
Wave equations
Nonlinear equations
restoration
wave equations
Restoration
nonlinear equations
aspect ratio
Aspect ratio
Damping
damping
thresholds
symmetry
Experiments

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

@article{989eff2d5e7e4293806a2083865e388e,
title = "Square patterns and secondary instabilities in driven capillary waves",
abstract = "Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from travelling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.",
author = "Milner, {Scott Thomas}",
year = "1991",
month = "1",
day = "1",
doi = "10.1017/S0022112091001970",
language = "English (US)",
volume = "225",
pages = "81--100",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

Square patterns and secondary instabilities in driven capillary waves. / Milner, Scott Thomas.

In: Journal of Fluid Mechanics, Vol. 225, 01.01.1991, p. 81-100.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Square patterns and secondary instabilities in driven capillary waves

AU - Milner, Scott Thomas

PY - 1991/1/1

Y1 - 1991/1/1

N2 - Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from travelling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.

AB - Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from travelling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.

UR - http://www.scopus.com/inward/record.url?scp=0026141889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026141889&partnerID=8YFLogxK

U2 - 10.1017/S0022112091001970

DO - 10.1017/S0022112091001970

M3 - Article

AN - SCOPUS:0026141889

VL - 225

SP - 81

EP - 100

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -