Oscillatory Instability in a Two-Fluid Benard Problem.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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 Earths mantle, which is sometimes based on the assumption that convection takes place in chemically uniform layers.
- Statistics and Probability
- Fluid Mechanics