Single-mode Rayleigh–Taylor instability in time-dependent rarefaction-driven flows

Rayleigh–Taylor instability (RTI) caused by rarefaction waves not only features variable acceleration but also incorporates time-dependent density, which introduces great challenges in predicting the finger growth behaviours. In this work, we propose a model for predicting the single-mode finger behaviours by extending the Layzer potential-flow framework to account for time-dependent acceleration and density. Relative to the previous models, the present model can evaluate the effect of time-dependent density on finger growth, and can describe the growth behaviours of both bubbles and spikes in rarefaction-driven RTI flows. In addition, the time-dependent curvature of the finger tip as it evolves from its initial value to the quasi-steady value is quantified. To validate the model, rarefaction-tube experiments and numerical simulations are conducted across a wide range of initial conditions. The results show that the present model can accurately capture the amplitude growth and curvature evolution of bubbles and spikes across various density ratios. Moreover, both the present model and experiments demonstrate that the continuous density reduction in rarefaction-driven flows causes larger asymptotic velocities of bubbles and spikes, leading to higher Froude numbers relative to those under constant or time-dependent acceleration.