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When a liquid slams into a solid, the intermediate gas is squeezed out at aspeed that diverges when approaching the moment of impact. Although there ismounting experimental evidence that instabilities form on the liquid interfaceduring such an event, understanding of the nature of these instabilities islimited. This study therefore addresses the stability of a liquid-gas interfacewith surface tension, subject to a diverging flow in the gas phase, where theliquid and the gas phase are both represented as potential fluids. We perform aKelvin-Helmholtz-type linear modal stability analysis of the surface to obtainan amplitude equation that is subsequently analysed in detail and applied totwo cases of interest for impact problems, namely, the parallel impact of awave onto a vertical wall, and the impact of a horizontal plate onto a liquidsurface. In both cases we find that long wavelengths are stabilisedconsiderably in comparison to what may be expected based upon classicalknowledge of the stability of interfaces subject to a constant gas flow. In theformer case, this leads to the prediction of a marginally stable wavelengththat is completely absent in the classical analysis. For the latter we findmuch resemblance to the classical case, with the connotation that theinstability is suppressed for smaller disk sizes. The study ends with adiscussion of the influence of gas viscosity and gas compressibility on therespective stability diagrams.

Linear stability analysis of a time-divergent slamming flow