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Long wavelength instabilities of square patterns

Long wavelength instabilities of square patterns
Long wavelength instabilities of square patterns
The long wavelength instabilities of square and rectangular planforms are studied analytically and numerically, using amplitude equations which describe the general interaction of two orthogonal coupled roll patterns. The zigzag and two-dimensional Eckhaus instabilities are found, and in addition it is discovered that the three-dimensional equivalent of the Eckhaus instability splits into two variants. The square Eckhaus instability is the direct equivalent of the two-dimensional case, whereas the rectangular Eckhaus instability is truly three-dimensional in character. In the case of square patterns, nonlinear phase diffusion equations are derived close to the onset of the instabilities. A short wavelength cross square mode is also discussed briefly.
0167-2789
198-223
Hoyle, Rebecca B.
e980d6a8-b750-491b-be13-84d695f8b8a1
Hoyle, Rebecca B.
e980d6a8-b750-491b-be13-84d695f8b8a1

Hoyle, Rebecca B. (1993) Long wavelength instabilities of square patterns. Physica D: Nonlinear Phenomena, 67 (1-3), 198-223. (doi:10.1016/0167-2789(93)90206-G).

Record type: Article

Abstract

The long wavelength instabilities of square and rectangular planforms are studied analytically and numerically, using amplitude equations which describe the general interaction of two orthogonal coupled roll patterns. The zigzag and two-dimensional Eckhaus instabilities are found, and in addition it is discovered that the three-dimensional equivalent of the Eckhaus instability splits into two variants. The square Eckhaus instability is the direct equivalent of the two-dimensional case, whereas the rectangular Eckhaus instability is truly three-dimensional in character. In the case of square patterns, nonlinear phase diffusion equations are derived close to the onset of the instabilities. A short wavelength cross square mode is also discussed briefly.

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More information

Published date: 1993
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 380306
URI: https://eprints.soton.ac.uk/id/eprint/380306
ISSN: 0167-2789
PURE UUID: 8273966f-93dd-4cfb-84eb-1ecc9b2d8b1c
ORCID for Rebecca B. Hoyle: ORCID iD orcid.org/0000-0002-1645-1071

Catalogue record

Date deposited: 12 Aug 2015 09:26
Last modified: 06 Jun 2018 12:33

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