Aspect-ratio-constrained Rayleigh–Taylor instability

Abstract

In this paper, we study turbulent mixing between two miscible fluids that is induced gravitationally by Rayleigh–Taylor instability in a tightly confined domain. In our experimental configurations, one lateral dimension is between two and three orders of magnitude smaller than the other. Our motivation is to examine the relationship between domain width and certain key flow statistics, as the geometric restriction changes in relative significance. We match our experiments with carefully-resolved numerical simulations and in order to impose appropriate initial conditions, we extend Taylor’s linear model of instability growth to characterise the influence of geometry on early modal development and use measured experimental data to inform our initialisation. We find that our experiments exhibit initial conditions with a k−1 spectral scaling of interfacial perturbation of volume fraction with a high degree of repeatability, where k denotes wavenumber. We discovered that our form of geometric restriction couples favourably with the spectral composition of our initial condition. We observe no early-stage transient relaxation towards self–similarity, because the instability already begins in that stable self-similar equilibrium, and this important special case has not previously been noticed despite decades of related research. We present our statistical observations from both experiment and numerical simulation as a validation resource for the community; such simulations are inexpensive to compute yet capture many dynamically significant properties.