Perturbation of a Multiple Eigenvalue in the Benard Problem for Two Fluid Layers.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In a recent paper, Renardy and Joseph study the Bernard problem for two layers of different fluids lying on top of each other and bounded by walls. Their study shows that, in contrast to the Benard problem for one fluid, the onset of instability can be oscillatory. The number of parameters involved in the problem is large, and there is yet no comprehensive picture of when the instability is oscillatory and when it is not. The study of limiting cases, accessible by perturbation methods, may be helpful in this respect. In this document, an analysis is given for the case when the properties of the two fluids are nearly equal and the fluids are allowed to slip at the boundaries. Author
- Numerical Mathematics
- Fluid Mechanics