Stability of unstably stratified shear flow between parallel plates

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Abstract
The linear stability of unstably stratified shear flows between two horizontal parallel plates has been investigated. The eigenvalue problem was solved numerically by making use of the expansion method in Chebyshev polynomials, and critical Rayleigh numbers were obtained accurately in the Reynolds number range of [0.01,100]. It was found that the critical Rayleigh number for two-dimensional disturbances increases with an increase of the Reynolds number. The result strongly supports previous stability analyses except for the analysis by Makino and Ishikawa (1985) in which a decrease of the critical Rayleigh number was obtained. For some cases, a discontinuity in the critical wavenumber occurs, due to the development of two extrema in the neutral stability boundary.

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