Bifurcating Instability of the Free Surface of a Ferrofluid
Consider a slab of ferrofluid bounded below by a fixed boundary and above by a vacuum. If the fluid is subjected to a vertically directed magnetic field of sufficient strength, surface waves appear. The equations which describe this phenomenon are derived. In the physical space no natural Banach spa...
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| Vydané v: | SIAM journal on mathematical analysis Ročník 14; číslo 4; s. 736 - 766 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Philadelphia
Society for Industrial and Applied Mathematics
01.07.1983
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| Predmet: | |
| ISSN: | 0036-1410, 1095-7154 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Consider a slab of ferrofluid bounded below by a fixed boundary and above by a vacuum. If the fluid is subjected to a vertically directed magnetic field of sufficient strength, surface waves appear. The equations which describe this phenomenon are derived. In the physical space no natural Banach space structure is available due to the free surface. In order to use the available bifurcation theory, a transformation of coordinates is made, mapping the surface flat. In the new coordinate system the equations define an operator between Banach spaces. The minimum eigenvalue of the linearized operator is the critical magnetic field strength where the planar surface loses stability. Using a generalized inverse of the Frechet derivative of the operator and the implicit function theorem, the existence of a nontrivial branch of solutions is proved. A local stability criterion is also obtained and applied to three periodic structures: rolls, squares and hexagons. |
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| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0036-1410 1095-7154 |
| DOI: | 10.1137/0514056 |