Initial-value problem for boundary layer flows

Abstract

The behavior of small disturbances in a boundary layer flow is studied. The initial-value problem is solved formally with Fourier–Laplace transforms, and an expression for the development of the velocity component normal to the wall is obtained. It is found that a disturbance evolves not only as discrete waves of the Tollmien–Schlichting type, but also has a portion described by a continuous spectrum. This portion is associated with a branch cut of the solution in the complex plane of the Laplace transform variable.