Interfacial Stability in a Two-Layer Benard Problem.

Abstract

A linear stability analysis of the benard problem for two layers of different fluids lying on top of each other and bounded by free surfaces is considered. The fluids are assumed to be similar and perturbation methods are used to calculate the eigenvalue in closed form. The case of the Rayleigh number and wavenumber of the disturbance being close to the first criticality of the one-fluid Benard problem has been investigated in a previous paper, and was found to exhibit both overstability and convective instability. In this paper, the Rayleigh number is assumed to be less than that of the first criticality of the one-fluid problem, and in this situation, overstability does not occur. An unexpected result is that by an appropriate choice of parameters, it is possible to find linearly stable arrangements with the more dense fluid on top. Keywords: Convective instability; Two-component flow; Interfacial stability; Navier stokes equations; Density; Boussinesq approximation. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1985
Accession Number
ADA158138

Entities

People

  • Y. Renardy

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Science
  • Conductivity
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Flow
  • Fluid Flow
  • Mechanical Properties
  • Navier Stokes Equations
  • Physical Properties
  • Prandtl Number
  • Shear Stresses
  • Stresses
  • Surface Properties
  • Surface Tension
  • Thermal Conductivity
  • Viscosity

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.