Global stability analysis of non-parallei flows

Abstract

Most shear flows are spatially developing, i.e., their velocity profile evolves as the flow proceeds downstream. Typically, as the Reynolds number increases, the laminar shear flow undergoes a linear instability, followed by an often complicated, and not completely understood, route to turbulence. Oftentimes, the flow might not undergo the different stages of instability, but directly becomes turbulent, through a process called bypass transition. The route which a flow chooses to become turbulent by depends upon many parameters like goemetry, free stream disturbances, etc. As with any work on flow stability and transition, this thesis also starts by referring to the work of Osborne Reynolds in 1883, which was the first systematic study on the stability of flow through pipes. The review paper by Jackson & Launder (2007) discusses the two important papers by Reynolds and his interactions with the referees, that have so greatly influenced the development of Engineering Fluid Mechanics over the past century.