Turbulence has been a topic of scientific research for years. Characterized by unorganized chaotic motion and irregular fluctuations, it persists as one of the most challenging topics in fluid mechanics despite volumes of documented research and crucial findings. This begs the question: What is turbulence and why is it so challenging? Turbulence research studies cover a wide spectrum of branches from fundamental flow propagation to different turbulence interactions. This research project investigates the simplest class of turbulent flow studies, homogeneous isotropic turbulence. In a quest to advance the fundamental understanding of turbulence physics, a direct numerical simulation tool is developed. The tool generates a turbulent periodic cube with vortical fluctuations and three interaction case studies. The evolution of the velocity in time is derived from the Navier-Stokes equations. These governing equations are integrated, along with initial and boundary conditions, to formulate turbulence. Fully-developed turbulence is achieved when the Tavoularis (1978) criterion of axial velocity variation is met. Output data sets are collected for numerical analysis. The turbulence periodic cube geometry is assessed for its applicability in this study. The simplified structure is found to be efficient and facilitated. The interaction case studies of shock-turbulence and detonation-turbulence are compared to an unforced flow interaction. The case studies are statistically analyzed and visualized yielding important conclusions on the effects of the fluctuations, heat release, detonation inherent length scale, and detonation intrinsic instability on the flow behavior. A mutual interaction is found between the turbulence structures and the strong detonation wave. An extension of the long-standing Tavoularis velocity skewness factor is suggested. The proposed velocity skewness vector quantifies the variation of the three velocity components in the three Cartesian coordinates. This comprehensive expression highlights the contribution of the three-dimensional velocity fluctuations to the turbulence state.