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The Rayleigh-Taylor instability is one of the most common and well studied phenomena in fluid dynamics. Despite research dating to the late 19th century, the non-linear dynamics of the interfacial instability are still not fully understood, particularly in the case when the two fluids have nearly the same density. It was recently demonstrated in this, the low- Atwood regime, that the idealized single-mode problem departs from established potential flow models in the form of a re-acceleration beyond the predicted terminal interface velocity. This thesis is an attempt to model that re-acceleration and, more broadly, the late time dynamics of the single-mode low-Atwood Rayleigh-Taylor instability. The approach taken here is based on buoyancy-drag models, which express a force balance between buoyancy and parasitic drag. The dynamical buoyancy-drag model is supplemented with a mixing model that dilutes the buoyant force over time. These models are written deliberately generally, with 8 unique coefficients. Three of these coefficients are solved for by equating the early time behavior with that of well established linear theories. The re- maining 5 coefficients are estimated by relating them to drag coefficients, friction factors, and geometric ratios in the interface shape. To evaluate the model and compute the 5 unknown coefficients more precisely, a set of direct numerical simulations are performed over the relevant parameter space. These simulations are first validated against experimental data. Then they are shown to converge and their resolutions are chosen such as to minimize computational cost given the accuracy scale of the model. The 5 coefficients are fit to the resulting data set, and the model achieves better than 2% error in the bubble height and 4% error in the volume of mixed fluid. Three coefficients are nominally independent of the parameterization of the problem, while two are shown to vary with the Rayleigh number and the diffusivity.


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