Instability and transition in the boundary layer

A theoretical model has been developed to describe the different stages of development in the transition of an incompressible laminar flow to its turbulent stage along a flat plate boundary. The transition is modelled as a three stage, sequential event that begins with the two dimensional Tollmein-Schlichting (T-S) wave disturbance. This is followed by the appearance of a longitudinal counterrotating vortex disturbance. The final stage of the transition is characterized by the appearance of the familiar wedge-shaped turbulent "bursts'. The first phase of the analysis involves the search for the saturation amplitude for the largest amplitude T-S waves for Reynolds numbers from 290 to 1160. A modified Stuart-Watson asymptotic method is used to obtain the neutra surface for the finite amplitude two dimensional self-excited traveling wave disturbance. This neutral surface is defined in the three-parameter space of Reynolds number (R), wavenumber and limiting amplitude (A) characteristics of the disturbance.