Dr Djoko Wirosoetisno djoko.wirosoetisno@durham.ac.uk
Associate Professor
Persistence of steady flows of a two-dimensional perfect fluid in deformed domains
Wirosoetisno, Djoko; Vanneste, Jacques
Authors
Jacques Vanneste
Abstract
The robustness of steady solutions of the Euler equations for two-dimensional, incompressible and inviscid fluids is examined by studying their persistence for small deformations of the fluid-domain boundary. Starting with a given steady flow in a domain D0, we consider the class of flows in a deformed domain D that can be obtained by rearrangement of the vorticity by an area-preserving diffeomorphism. We provide conditions for the existence and (local) uniqueness of a steady flow in this class when D is sufficiently close to D0 in Ck,α, k ≥ 3 and 0 < α < 1. We consider first the case where D0 is a periodic channel and the flow in D0 is parallel and show that the existence and uniqueness are ensured for flows with non-vanishing velocity. We then consider the case of smooth steady flows in a more general domain D0. The persistence of the stability of steady flows established using the energy–Casimir or, in the parallel case, the energy–Casimir–momentum method, is also examined. A numerical example of a steady flow obtained by deforming a parallel flow is presented.
Citation
Wirosoetisno, D., & Vanneste, J. (2005). Persistence of steady flows of a two-dimensional perfect fluid in deformed domains. Nonlinearity, 18(6), 2657-2680. https://doi.org/10.1088/0951-7715/18/6/013
Journal Article Type | Article |
---|---|
Publication Date | 2005-11 |
Deposit Date | Feb 29, 2008 |
Journal | Nonlinearity |
Print ISSN | 0951-7715 |
Electronic ISSN | 1361-6544 |
Publisher | IOP Publishing |
Peer Reviewed | Peer Reviewed |
Volume | 18 |
Issue | 6 |
Pages | 2657-2680 |
DOI | https://doi.org/10.1088/0951-7715/18/6/013 |
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