The nonlinear growth of Tollmien-Schlichting disturbances in a boundary layer is considered as an initial-value problem, for the unsteady two- dimensional triple deck, and computational and analytical solutions are presented.
On the analytical side, the nonlinear properties of relatively high- frequency/high-speed disturbances are discussed. The disturbances travel at the group velocity and their amplitude is controlled by a generalized cubic Schrödinger equation, during a first stage of the nonlinear development. Computationally, two forms of numerical solution of the triple-deck problem, one spectral, the other finite-difference, are given. The results from each form tend to support the conclusions of the high-frequency analysis for initial-value problems, and recent calculations of the two-dimensional unsteady Navier-Stokes equations also provide some backing. One implication is that the unsteady planar interacting-boundary-layer equations, or a composite version, can capture much of the physics involved in the beginnings of boundary-layer transition although, again, three-dimensionality is undoubtedly an important element which will need to be incorporated eventually.