Taylor instability of a flat isentropic layer with isobaric boundaries
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A study is made of the stability of the hydrostatic equilibrium of a layer of gas with flat boundaries in a uniform gravity field. A similar problem was considered by Plesset and Hsieh , who considered only the short-wavelength correction to the incompressible case, i.e., made a calculation in the approximation of small λ/L, and calculated the first two terms in the expansion of the growth rate with respect to the parameter λ/L, where λ is the wavelength and L the thickness of the layer. In the present paper, the growth rate of the Taylor instability is found for the case of isobaric boundaries for arbitrary ratio λ/L. The calculation is made for the case when there is not necessarily a vacuum at the top of the layer. An error made by Plesset and Hsieh  in selecting the solution at the interface with the vacuum is corrected. It is shown that in the case of an isentropic layer the Taylor mode is the only unstable one.
KeywordsGrowth Rate Gravity Field Hydrostatic Equilibrium Taylor Instability Incompressible Case
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- 1.M. S. Plesset and D. Y. Hsieh, “General analysis of the stability of superposed fluids,” Phys. Fluids,7, 1099 (1964).Google Scholar