A plot of vs wavenumber for neutral modes with equal layer depths showing morphological instability with flow. The solid curve is a direct mode and the dashed curve is an oscillatory mode. A small-wavenumber approximation is indicated by dots.
A plot of vs wavenumber for neutral modes with layer depths and showing morphological instability with flow. The solid curve is a direct mode and the dashed curves are oscillatory modes. The round data points indicate the results from a small-wavenumber approximation for the direct mode, and the square data points on the oscillatory branch correspond to analytical results for a morphological stability analysis in which flow is neglected.
A plot of vs layer depth for and and a wavenumber . The solid curves are the small-wavenumber approximation and the data points are the full numerical solution. There is a pole for .
A plot of vs wavenumber for and various values of showing morphological stability without flow. The dashed line is , the small-wavenumber expansion result for small positive values of . The numbers in the figure denote the value of used to generate the adjacent curve. The four additional curves that lie in the narrow region correspond to values , , , and from left to right.
Dimensionless properties used in numerical calculations. Material properties are based on values used for the aluminum-indium system (Ref. 5) with , but further idealized by taking , and .
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