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Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container
Lapuerta González, María Victoria and Mancebo, Francisco J. and Vega de Prada, José Manuel
Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container.
"Nonlinear Analysis: Theory, Methods & Applications", v. 47
||Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container
Lapuerta González, María Victoria
Mancebo, Francisco J.
Vega de Prada, José Manuel
|Título de Revista/Publicación:
||Nonlinear Analysis: Theory, Methods & Applications
||Rayleigh-Taylor instability, stabilization by forced vibration, free
1991 MSC: 76E30, 76E17, 35K55, 35B32, 35B35, 35B40
1 Introduction and formulation
The Rayleigh-Taylor instability  appears when a heavy fluid is accelerated towards a lighter one and
has a basic interest in Fluid Mechanics. The simplest configuration exhibiting this instability is that
in which a horizontal heavy fluid layer (e.g., water or mineral oil) is supported by a lighter fluid (e.g.,
air); the destabilizing acceleration is provided by gravity. In this configuration, the instability can be
counterbalanced by an imposed vertical vibration of the container, as already shown experimentally
 and theoretically -. The main object of this paper is to provide a weakly nonlinear theory
||E.T.S.I. Aeronáuticos (UPM)
||Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
|Creative Commons Licenses:
||Recognition - No derivative works - Non commercial
We consider a horizontal liquid layer supported by air in a wide (as compared to depth) container, which is vertically vibrated with an appropriately large frequency, intending to counterbalance the Rayleigh-Taylor instability of the fíat, rigid-body vibrating state. We apply a long-wave, weakly-nonlinear analysis that yields a generalized Cahn-Hilliard equation for the evolution of the fluid interface, with appropriate boundary conditions obtained by a boundary layer analysis. This equation shows that the stabilizing effect of vibration is like that of surface tensión, and is used to analyze the linear stability of the fíat state, and the local bifurcation at the instability threshold.
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