Sideband instability and modulations of Faraday waves

S P  Decent; A D D  Craik

doi:10.1016/S0165-2125(98)00048-1

Sideband instability and modulations of Faraday waves

S P Decent, A D D Craik

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Three-mode interaction equations are derived for Faraday waves in a long rectangular container. Two water depths are studied, revealing very different behaviour. Our equations include conservative and non-conservative cubic nonlinear terms, and quintic conservative nonlinear terms. Instability of a single standing wave to neighbouring modes is examined. Resultant three-mode interactions display rich structure, with fast and slow timescales. For the smaller depth, but not the greater, recurrent nearly calm intervals are separated by strong wave activity. Our results agree quite well with experimental findings of Craik and Armitage [Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank, Fluid Dyn. Res. 15 (1995) 129-143] and with unpublished observations by Armitage, Craik and Sterratt, here briefly described. (C) 1999 Elsevier Science B.V. All rights reserved.

Original language	English
Pages (from-to)	43-55
Number of pages	13
Journal	Wave Motion
Volume	30
Issue number	1
DOIs	https://doi.org/10.1016/S0165-2125(98)00048-1
Publication status	Published - Jul 1999

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title = "Sideband instability and modulations of Faraday waves",

abstract = "Three-mode interaction equations are derived for Faraday waves in a long rectangular container. Two water depths are studied, revealing very different behaviour. Our equations include conservative and non-conservative cubic nonlinear terms, and quintic conservative nonlinear terms. Instability of a single standing wave to neighbouring modes is examined. Resultant three-mode interactions display rich structure, with fast and slow timescales. For the smaller depth, but not the greater, recurrent nearly calm intervals are separated by strong wave activity. Our results agree quite well with experimental findings of Craik and Armitage [Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank, Fluid Dyn. Res. 15 (1995) 129-143] and with unpublished observations by Armitage, Craik and Sterratt, here briefly described. (C) 1999 Elsevier Science B.V. All rights reserved.",

author = "Decent, {S P} and Craik, {A D D}",

year = "1999",

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doi = "10.1016/S0165-2125(98)00048-1",

language = "English",

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journal = "Wave Motion",

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T1 - Sideband instability and modulations of Faraday waves

AU - Decent, S P

AU - Craik, A D D

PY - 1999/7

Y1 - 1999/7

N2 - Three-mode interaction equations are derived for Faraday waves in a long rectangular container. Two water depths are studied, revealing very different behaviour. Our equations include conservative and non-conservative cubic nonlinear terms, and quintic conservative nonlinear terms. Instability of a single standing wave to neighbouring modes is examined. Resultant three-mode interactions display rich structure, with fast and slow timescales. For the smaller depth, but not the greater, recurrent nearly calm intervals are separated by strong wave activity. Our results agree quite well with experimental findings of Craik and Armitage [Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank, Fluid Dyn. Res. 15 (1995) 129-143] and with unpublished observations by Armitage, Craik and Sterratt, here briefly described. (C) 1999 Elsevier Science B.V. All rights reserved.

AB - Three-mode interaction equations are derived for Faraday waves in a long rectangular container. Two water depths are studied, revealing very different behaviour. Our equations include conservative and non-conservative cubic nonlinear terms, and quintic conservative nonlinear terms. Instability of a single standing wave to neighbouring modes is examined. Resultant three-mode interactions display rich structure, with fast and slow timescales. For the smaller depth, but not the greater, recurrent nearly calm intervals are separated by strong wave activity. Our results agree quite well with experimental findings of Craik and Armitage [Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank, Fluid Dyn. Res. 15 (1995) 129-143] and with unpublished observations by Armitage, Craik and Sterratt, here briefly described. (C) 1999 Elsevier Science B.V. All rights reserved.

U2 - 10.1016/S0165-2125(98)00048-1

DO - 10.1016/S0165-2125(98)00048-1

M3 - Article

SN - 0165-2125

VL - 30

SP - 43

EP - 55

JO - Wave Motion

JF - Wave Motion

IS - 1

ER -

Sideband instability and modulations of Faraday waves

Abstract

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