dorsal/arxiv
View SchemaSteady and Oscillatory Side-Band Instabilities in Marangoni Convection with Deformable Interface
| Authors | A. A. Golovin, A. A. Nepomnyashchy, L. M. Pismen, H. Riecke |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9510005 |
| URL | https://arxiv.org/abs/patt-sol/9510005 |
Abstract
The stability of Marangoni roll convection in a liquid-gas system with deformable interface is studied in the case when there is a nonlinear interaction between two modes of Marangoni instability: long-scale surface deformations and short-scale convection. Within the framework of a model derived previously, it is shown that the nonlinear interaction between the two modes substantially changes the width of the band of stable wave numbers of the short-scale convection pattern as well as the type of the instability limiting the band. Depending on the parameters of the system, the instability can be either long- or short-wave, either monotonic or oscillatory. The stability boundaries strongly differ from the standard ones and sometimes exclude the band center. The long-wave limit of the side-band instability is studied in detail within the framework of the phase approximation. It is shown that the monotonic instability is always subcritical, while the long-wave oscillatory instability can be supercritical, leading to the formation of either travelling or standing waves modulating the pattern wavelength and the surface deformation.
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"abstract": "The stability of Marangoni roll convection in a liquid-gas system with\ndeformable interface is studied in the case when there is a nonlinear\ninteraction between two modes of Marangoni instability: long-scale surface\ndeformations and short-scale convection. Within the framework of a model\nderived previously, it is shown that the nonlinear interaction between the two\nmodes substantially changes the width of the band of stable wave numbers of the\nshort-scale convection pattern as well as the type of the instability limiting\nthe band. Depending on the parameters of the system, the instability can be\neither long- or short-wave, either monotonic or oscillatory. The stability\nboundaries strongly differ from the standard ones and sometimes exclude the\nband center. The long-wave limit of the side-band instability is studied in\ndetail within the framework of the phase approximation. It is shown that the\nmonotonic instability is always subcritical, while the long-wave oscillatory\ninstability can be supercritical, leading to the formation of either travelling\nor standing waves modulating the pattern wavelength and the surface\ndeformation.",
"arxiv_id": "patt-sol/9510005",
"authors": [
"A. A. Golovin",
"A. A. Nepomnyashchy",
"L. M. Pismen",
"H. Riecke"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Steady and Oscillatory Side-Band Instabilities in Marangoni Convection with Deformable Interface",
"url": "https://arxiv.org/abs/patt-sol/9510005"
},
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