Data Analysis of Rayleigh-Taylor Unstable Flows

Rayleigh-Taylor and Richtmyer-Meshkov instabilities (RTI and RMI) occur when afluid interface between fluids of different densities is accelerated against the density gradient. RTI/RMI plays an important role in the dynamics of fluids and plasmas on microscopic scales, such as inertial confinement fusion, through astronomical scales, such as supernova explosions. These problems have been studied for decades, yet it remains a challenge to observe, model, and describe RTI/RMI mathematically. Without the tools used to analyze stable equilibrium, we must find more robust analyses. This work uses robust data analysis techniques to systematically study RT unstable flows. We report a thorough analysis of experimental data in supernova experiments conducted at high powered laser facilities, evaluating what information experiments and simulations may tell us about the fundamentals of RTI and RT mixing in high energy density plasmas by comparing the data with rigorous theoretical approaches. We investigate the statistically unsteadiness of RT mixing by numerically modeling the set of stochastic nonlinear differential equations which govern the rate of change of momentum in a packet of fluid undergoing RT instability. By analyzing the modeled solutions, we measure the influence of fluctuations on measurable quantities, find new characteristic values which may be used as to diagnose the regime of an experiment or simulation, and measure the spectra of fluctuations as they propagate throughout the system. We study the effect of the initial perturbation amplitude on the RMI interfacial dynamics using Single Particle Hydrodynamics simulations. The compound motion of the interface and bulk fluid ow is measured, an empirical model is found to describe data, and we find an upper bound for the amount of energy deposited to the interface. There exists a plethora of data that may still be analyzed systematically, as exemplified in this thesis. Future work may improve the fits of experimental data by exploring well designed parameter spaces, model additional stochastic effects, and measure small scale features of ow quantities in simulations.