The problem of describing transition in wall bounded shear flows such as channel and boundary layer flows is an important and old problem in Hydrodynamic Stability. Classical linear hydrodynamic stability theories provides predictions that are at odds with most experiments where ``natural'' transition occurs. However, in the past decade it has become recognized that a new kind analysis of the linearized Navier-Stokes equations yields much more satisfactory answers. It turns out that the non-normality of the linear dynamical operator in strongly sheared flows plays a much more important role in stability than do its eigenvalues.

In this talk, we will review this new hydrodynamic stability theory from the point of view of quantifying uncertainty. The linearized Navier-Stokes equations in strongly sheared flows exhibit remarkable sensitivity to dynamical perturbations and external forcing or noise. We will argue that the right kind stability analysis must take this uncertainty explicitly into account. We will also point out important connections with modern Robust Control Theory, were analysis of uncertainty effects on stability has been heavily studied.

We will show how this theory predicts the large perturbation energy growth observed in boundary layer flows, and the ubiquitous coherent structures of stream-wise vortices and streaks. We will also illustrate how distributed wall roughness can act as a generator of flow disturbances which then initiate transition scenarios. Finally, our results motivate us to propose an input-output theory of shear flow turbulence.