This dissertation seeks to contribute to the broader understanding of stratified turbulent systems through high fidelity numerical simulations of idealized problems. We begin by studying turbulence in the presence of a density interface in isolation, where the complication of a background mean flow (specifically, the shear stress induced by such a mean flow) is removed. The simulations are reminiscent of oscillating grid turbulence (OGT) experiments popular in the latter half of the twentieth century. We revisit some classical scaling results of those experiments and offer some new insights gained through our simulations.