The transient period for boundary layer disturbances

The onset of transition in a boundary layer is dependent on the initializat ion and interaction of disturbances in a laminar flow. Here, theory and ful l Navier-Stokes simulations focus on the transient period just after distur bances enter the boundary layer. The temporal evolution of disturbances wit hin a boundary layer is investigated by examining a series of initial value problems. In each instance, the complete spectra (i.e. the discrete and th e continuum) are included so that the solutions can be completely arbitrary . Both numerical and analytical solutions of the linearized Navier-Stokes e quations subject to the arbitrary initial conditions are presented. The tem poral evolution of disturbances during the transient period are compared wi th the spatial evolution of the same disturbances and a strong correlation between the two approaches is demonstrated indicating that the theory may b e used for the transient period of disturbance evolution. The theory and si mulations demonstrate that strong amplification of the disturbances can occ ur as a result of the inclusion of the continuum in the prediction of distu rbance evolution. The results further show that any approach proposed for u se in bypass boundary layer transition must include the transient growth th at results from the continuum. Finally, although a connection between tempo ral and spatial evolution in the transient period has been demonstrated, a theoretical basis as an explanation for this connection remains the focus o f additional study.