ISMAEL DJIBRILLA BOUREIMA. A Numerical Study of Inhomogeneous Variable-Density Turbulence in Planar and Convergent Geometries. (Under the direction of DR. PRAVEEN RAMAPRABHU)Hydrodynamic instabilities govern the growth of perturbations at the interfaces between two fluids of different densities when subjected to an acceleration. The applied external acceleration can lead to the Rayleigh-Taylor (RT) instability, or when an impulsive acceleration in the form of an incident shock is applied, it leads to the Richtmyer-Meshkov (RM) instability. Such hydrodynamic instabilities, when allowed to develop, eventually lead to a turbulent state, characterized by vigorous mixing between the fluids. However, since the density difference between the fluids is finite, the turbulent flow is referred to as variable-density turbulence and is fundamentally different from its constant density counterpart. Such flows are observed in several natural and man-made situations including mixing in the upper atmosphere, supernovae explosions, nuclear fusion and shock-powered propulsion devices. A broad category of such flows was investigated using numerical simulations, enabled by multiple continuum codes, and the results of the study will be discussed. Properties of variable density turbulence were studied in detail through the following flow configurations: Rayleigh-Taylor turbulence, doubly-shocked Richtmyer-Meshkov instability, and turbulence in a confined spherical implosion. These flows represent varying degrees of external forcing and anisotropy, and thus provide a framework to understand the response of turbulent properties to these variations of interest to engineering applications. Such studies can be instrumental in improving current turbulence models or in manipulating mixing to achieve engineering objectives in applications. Numerical results from RT-turbulence including profiles of the turbulent mass flux, density-specific volume correlation and the turbulent kinetic energy were compared with a two-point spectral turbulence model. The double-shocked RM problem is of relevance to recent experiments at the National Ignition Facility in which multiple shocks whose strength and timing could be optimized, were used to maximize the fuel areal density and improve the neutron yield. In our hydrodynamic simulations of the double-shocked RM problem, we find the memory of the initial conditions at the instance of second shock recedes over a self-similar timescale, resulting in nearly universal growth rates at late times. Finally, we investigate the properties of variable-density turbulence occurring within an imploding mixing layer confined by spherical geometry.