Summary
The instability of a plane compressible gas sheet in a quiescent viscous liquid medium of infinite expanse has been studied. It is found that there exist two unstable modes of disturbances, sinuous and varicose. For temporal instability, sinuous disturbance is stable if the gas Weber number, defined as the ratio of aerodynamic to capillary forces, is less than unity, varicose mode controls the instability process except for large Weber numbers when both modes become equally important, and gas compressibility effect always enhances instability development and induces an additional range of unstable wave numbers. For spatial-temporal evolution of disturbances, it is found that convective instability does not exist at all and the instability of plane gas sheets is always absolute in nature, which is strikingly opposite to the instability of plane liquid sheets. The absolutely unstable disturbance is found always temporally growing, although it may be spatially growing or decaying depending on flow conditions. Gas compressibility always enhances and liquid viscosity damps out both the temporal and the spatial part of absolute instability growth rate. Although the Weber number always promotes the temporal growth rate of absolute instability, it has a dual effect of enhancing and inhibiting the spatial growth rate.
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Li, X., Bhunia, A. Instability of plane compressible gas sheets. Acta Mechanica 123, 117–133 (1997). https://doi.org/10.1007/BF01178405
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DOI: https://doi.org/10.1007/BF01178405