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 (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.

Description

Title: Weakly-nonlinear analysis of the Rayleigh–Taylor instability in a vertically vibrated, large aspect ratio container
Author/s:
  • Lapuerta González, María Victoria
  • Mancebo, Francisco J.
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Nonlinear Analysis: Theory, Methods & Applications
Date: August 2001
ISSN: 0362-546X
Volume: 47
Subjects:
Freetext Keywords: 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
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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.

More information

Item ID: 6013
DC Identifier: http://oa.upm.es/6013/
OAI Identifier: oai:oa.upm.es:6013
DOI: 10.1016/S0362-546X(01)00468-0
Official URL: http://www.sciencedirect.com/science/journal/0362546X
Deposited by: Memoria de Investigacion 2
Deposited on: 15 Feb 2011 12:32
Last Modified: 20 Apr 2016 14:40
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