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Stability of some stationary solutions to the forced KdV equation with one or two bumps ArchiMer
Chardard, Frederic; Dias, Frederic; Nguyen, Hai Yen; Vanden-broeck, Jean-marc.
Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The first-order approximation of long nonlinear surface waves over one or two bumps results in a forced Korteweg-de Vries (fKdV) equation. Solutions of the stationary fKdV equation are constructed and their stability is studied, either analytically or numerically. These various solutions include solitary waves over a single bump, solitary waves with two humps over a double bump, table-top solutions over a double bump and fronts.
Tipo: Text Palavras-chave: Forced Korteweg-de Vries equation; Free-surface flows; Numerical simulations; Stability; Topography.
Ano: 2011 URL: http://archimer.ifremer.fr/doc/00037/14873/12348.pdf
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Slow quasigeostrophic unstable modes of a lens vortex in a continuously stratified flow ArchiMer
Nguyen, Hai Yen; Hua, Bach-lien; Schopp, Richard; Carton, Xavier.
This work addresses the linear dynamics underlying the formation of density interfaces at the periphery of energetic vortices, well outside the vortex core, both in the radial and axial directions. We compute numerically the unstable modes of an anticyclonic Gaussian vortex lens in a continuously stratified rotating fluid. The most unstable mode is a slow mode, associated with a critical layer instability located at the vortex periphery. Although the most unstable disturbance has a characteristic vertical scale which is comparable to the vortex height, interestingly, the critical levels of the successively fastest growing modes are closely spaced at intervals along the axial direction that are much smaller than the vortex height.
Tipo: Text Palavras-chave: Quasigeostrophic model; Vortices; Stratified flow; Critical level; Flow instability.
Ano: 2012 URL: http://archimer.ifremer.fr/doc/00074/18520/16331.pdf
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