Boundary-layer stability and laminar-to-turbulent transition have been studied for decades in various flows. Many useful computational techniques have emerged for basic research, but only a few of these techniques have evolved into engineering tools. Furthermore, the basic research has moved from flat plates to BOLT and HIFiRE-5, rather complex geometries. As the basic research community begins to move toward more realistic engineering designs, there seems to be an opportunity to reassess the applicability of basic research computational techniques to engineering. BOLT and HIFiRE-5 are the focus of this dissertation. The goal is to use the parabolized stability equations and spatial BiGlobal theory to understand key parts of their transition processes. It is shown that these geometries are stationary-crossflow dominant. Furthermore, the power and utility of the nonlinear parabolized stability equations is shown here and shows that it can be a key partner with direct numerical simulations and experiments toward the understanding and modeling of the laminar-to-turbulent transition problem, and it is proposed that this technique has evolved quite nicely and can be used for real application. The parabolized stability equations are used for primary instability analysis and spatial BiGlobal theory is used for secondary instability analysis. The stationary-crossflow instability and its secondary instabilities are the focus, but other instabilities are examined. A physics-based technique to model the heating rates of nonlinearly developing stationary crossflow is proposed. Furthermore, it is demonstrated that coupling nonlinear parabolized stability equations with spatial BiGlobal theory could provide a generalized technique to predict transition onset in flows with stationary crossflow as the dominant mechanism. The transition onset location is predicted by the location of the secondary instability neutral point. Moreover, the observed amplification of the secondary instabilities could potentially be the predictor for breakdown to turbulence. There is a strong emphasis on validation with ground and flight tests and verification with direct numerical simulations. The goal is that these results will provide insight for future computational, ground, and flight work.
