Oscillatory Instability in a Two-Fluid Benard Problem.

Abstract

Flows involving two incompressible viscous fluids exhibit nonuniqueness in the sense that many interface positions are allowed when their densities are equal. Two-fluid flows also have quite different dynamical features from one-fluid flows. The one-fluid Benard problem in which the fluid, lying between parallel horizontal plates, is heated from below has a static solution for which a linear stability analysis yields no complex eigenvalues. In this paper we show that when two fluids are involved, the arrangement in horizontal layers can have complex eigenvalues at criticality and therefore can sustain disturbances which are oscillatory in time. This may have application to the theory of convection in the Earth's mantle, which is sometimes based on the assumption that convection takes place in chemically uniform layers.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1984
Accession Number
ADA142792

Entities

People

  • D. D. Joseph
  • Y. Renardy

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Convection
  • Eigenvalues
  • Equations
  • Flow
  • Fluid Flow
  • Fluid Mechanics
  • Instability
  • Mathematics
  • Shear Flow
  • Standing Waves
  • Surface Properties
  • Surface Tension
  • Temperature Gradients
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.