Interfacial stability in a twolayer 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 onefluid 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 onefluid 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.
 Publication:

Technical Summary Report Wisconsin Univ
 Pub Date:
 April 1985
 Bibcode:
 1985wisc.reptS....R
 Keywords:

 Approximation;
 Convective Flow;
 Interface Stability;
 Surface Layers;
 Surface Stability;
 Density (Mass/Volume);
 Eigenvalues;
 Flow Stability;
 Linear Systems;
 NavierStokes Equation;
 Perturbation Theory;
 Fluid Mechanics and Heat Transfer