Kahler Geometry and Burgers' Vortices
We study the Navier-Stokes and Euler equations of incompressible hydrodynamics. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation in two spatial dimensions using Monge-Ampere structures. In two dimensional flo...
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| Datum: | 2009 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2009
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| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/6310 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Kahler Geometry and Burgers' Vortices / I. Roulstone, B. Banos, J.D. Gibbon, V.N. Roubtsov // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 303-321. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We study the Navier-Stokes and Euler equations of incompressible hydrodynamics. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation in two spatial dimensions using Monge-Ampere structures. In two dimensional flows where the Laplacian of the pressure is positive, a Kahler geometry is described on the phase space of the fluid; in regions where the Laplacian of the pressure is negative, a product structure is described. These structures can be related to the ellipticity and hyperbolicity (respectively) of a Monge-Ampere equation. We then show how this structure can be extended to a class of canonical vortex structures in three dimensions. |
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