Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container

Lapuerta González, María Victoria; Mancebo, Francisco J. y Vega de Prada, José Manuel (2001). Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container. "Nonlinear Analysis: Theory, Methods & Applications", v. 47 (n. 5); pp. 3515-3520. ISSN 0362-546X. https://doi.org/10.1016/S0362-546X(01)00468-0.

Descripción

Título: Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container
Autor/es:
  • Lapuerta González, María Victoria
  • Mancebo, Francisco J.
  • Vega de Prada, José Manuel
Tipo de Documento: Artículo
Título de Revista/Publicación: Nonlinear Analysis: Theory, Methods & Applications
Fecha: Agosto 2001
Volumen: 47
Materias:
Palabras Clave Informales: Rayleigh-Taylor instability, stabilization by forced vibration, free surface flows. 1991 MSC: 76E30, 76E17, 35K55, 35B32, 35B35, 35B40 1 Introduction and formulation The Rayleigh-Taylor instability [1] 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 [2] and theoretically [3]-[4]. The main object of this paper is to provide a weakly nonlinear theory
Escuela: E.T.S.I. Aeronáuticos (UPM) [antigua denominación]
Departamento: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

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.

Más información

ID de Registro: 6013
Identificador DC: http://oa.upm.es/6013/
Identificador OAI: oai:oa.upm.es:6013
Identificador DOI: 10.1016/S0362-546X(01)00468-0
URL Oficial: http://www.sciencedirect.com/science/journal/0362546X
Depositado por: Memoria de Investigacion 2
Depositado el: 15 Feb 2011 12:32
Ultima Modificación: 20 Abr 2016 14:40
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