Abstract: Temporal instability analysis of a power-law sheet in a gas velocity oscillation field was performed with linear stability analysis. The oscillation of gas velocity induced the momentum equation to be a Hill equation with a time period coefficient, which was solved using Floquet theory. For different oscillation amplitudes and frequencies, the effects of the generalized Reynolds number, power-law index and dimensionless velocity factor on various unstable regions were studied. Results show that the increase of the oscillation amplitude or the decrease of the oscillation frequency will increase the number of unstable regions of the sheet, and the maximum growth rate, dominant wave number and cut-off wave number of the Kelvin-Helmholtz (K-H) unstable region increase with the increase of the oscillation amplitude and frequency. The increase in generalized Reynolds number, power-law index and dimensionless velocity factor enhances the instability of the K-H unstable region, causing the growth rate in the parametric instability region to decrease first and then increase. The variations of the oscillation amplitude do not change the rheological parameters corresponding to the transition of the maximum growth rate. When the oscillation frequency is small, the increase of power-law index or dimensionless velocity factor leads to monotonous increase of the maximum growth rate in the parametric instability region.

Key words: power-law fluid, planar sheets, velocity oscillations, Floquet theory, parametric instability