Abstract
Instabilities are often the precursors of transition to turbulent fluid motion in wall-bounded shear flows. This review motivates and presents mathematical tools for detecting and quantifying instability mecha- nism's - of both modal and non-modal type - in shear flows. The role of these instabilities during the transition process is illustrated, and extensions of the tools to capture unsteady effects, spatially evolving flows and inhomogeneous coordinate directions are given.