Understanding, predicting and eventually delaying transition to turbulence in fluid flows have been challenging issues for scientists ever since the pioneering work of Osborne Reynolds in 1883. These problems have mostly been addressed using the hydrodynamic linear stability theory. Yet, due to limited computational resources, linear stability analyses have essentially relied until recently on strong simplification hypotheses such as the “parallel flow” assumption. In this framework, known as “local stability theory”, only the stability of flows with strong academic interest but limited practical applications can be investigated. However, over the course of the past decade, simplification hypotheses have been relaxed from the “parallel flow” assumption to a two-dimensionality assumption of the flow resulting in what is now known as the “global stability theory”. This new framework allows one to investigate the instability and transition mechanisms taking place in more realistic flows. More particularly, the stability of strongly non-parallel flows exhibiting separation, a common feature of numerous flows of practical interest, can now be studied. Moreover, with the continuous increase of computational power available and the development of new iterative eigenvalue algorithms, investigating the global stability of fully three-dimensional flows, for which no simplification hypothesis is necessary, is now feasible. Following the work presented in 2008 by Bagheri et al., the aim of the present thesis is thus to develop the tools mandatory to investigate the stability of 3D flows. Three flow configurations have been chosen to illustrate the new investigation capabilities brought by global stability theory when it is applied to realistic three-dimensional flows: i) the flow within a cuboid lid-driven cavity, ii) the flow within an asymmetric stenotic pipe and iii) the boundary layer flow developing over a cylindrical roughness element mounted on a flat plate. Each of these flows have different practical applications ranging from purely academic interests to biomedical and aerodynamical applications. They also allow us to put in the limelight different aspects and possible limitations of the various tools developed during this PhD thesis.

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