Rayleigh-Taylor turbulence in its many shapes and sizes: understanding self-similar growth using statistically stationary minimal flow units

Self-similar Rayleigh-Taylor (RT) turbulence is studied using statistically stationary RT simulations of varying aspect ratios. Two key steps are taken to achieve flow stationarity. First, a coordinate transformation based on self-similar scaling is applied to the governing equations. Second, the transformed equations are evaluated at a specific mixing layer height. The resulting equations simulate statistically stationary RT (SRT) flow. In SRT flow, the mixing layer height, h, reaches a stationary value, and flow structures are observed to grow laterally until they reach the domain size, L. Leveraging these box-filling tendencies, the lateral domain length is varied at constant mixing layer height to generate SRT minimal flow units (MFUs) of different aspect ratios, h/L. Growth parameters, mixedness, correlation lengths, and planar-averaged statistics are presented as a function of aspect ratio and supported by theoretical scaling analyses. Finally, these SRT results are considered within the context of traditional temporally growing RT (TRT) flow. In TRT flow, observed values for the self-similar growth parameter, α, span a large range of values (0.02 - 0.12). This lack of agreement is commonly attributed to differences in initial conditions. We show that SRT MFUs can indeed reproduce flow dynamics with a similar range of α, establishing a possible relationship between the aspect ratio of a SRT flow with the initial conditions of a TRT flow.