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Phase instabilities of oscillatory standing squares and alternating rolls

Phase instabilities of oscillatory standing squares and alternating rolls
Phase instabilities of oscillatory standing squares and alternating rolls
The stability of standing squares and alternating rolls is investigated within the framework of the lowest-order amplitude equations describing the interaction of right-, left-, up-, and down-traveling waves on a square lattice. It is found that a standing-square or alternating-roll pattern is subject to a stationary rectangular phase instability and an oscillatory phase instability. The rectangular mode is locally equivalent to a stretching along one coordinate axis and contraction along the orthogonal axis. The oscillatory instability is locally equivalent to the coordinate axes rotating towards or away from each other, and leads to quasiperiodic temporal oscillations of the bifurcated state.
1539-3755
2875-2880
Hoyle, R. B.
e980d6a8-b750-491b-be13-84d695f8b8a1
Hoyle, R. B.
e980d6a8-b750-491b-be13-84d695f8b8a1

Hoyle, R. B. (1994) Phase instabilities of oscillatory standing squares and alternating rolls. Physical Review E, 49 (4), 2875-2880. (doi:10.1103/PhysRevE.49.2875).

Record type: Article

Abstract

The stability of standing squares and alternating rolls is investigated within the framework of the lowest-order amplitude equations describing the interaction of right-, left-, up-, and down-traveling waves on a square lattice. It is found that a standing-square or alternating-roll pattern is subject to a stationary rectangular phase instability and an oscillatory phase instability. The rectangular mode is locally equivalent to a stretching along one coordinate axis and contraction along the orthogonal axis. The oscillatory instability is locally equivalent to the coordinate axes rotating towards or away from each other, and leads to quasiperiodic temporal oscillations of the bifurcated state.

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More information

Published date: 1 April 1994
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 380304
URI: https://eprints.soton.ac.uk/id/eprint/380304
ISSN: 1539-3755
PURE UUID: fb5d0aad-8701-4f6a-96bc-cabfc1124556
ORCID for R. B. Hoyle: ORCID iD orcid.org/0000-0002-1645-1071

Catalogue record

Date deposited: 12 Aug 2015 09:23
Last modified: 06 Jun 2018 12:33

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