The transient period for boundary layer disturbances

Abstract

The onset of transition in a boundary layer is dependent on the initialization and interaction of disturbances in a laminar flow. Here, theory and full Navier–Stokes simulations focus on the transient period just after disturbances enter the boundary layer. The temporal evolution of disturbances within a boundary layer is investigated by examining a series of initial value problems. In each instance, the complete spectra (i.e. the discrete and the continuum) are included so that the solutions can be completely arbitrary. Both numerical and analytical solutions of the linearized Navier–Stokes equations subject to the arbitrary initial conditions are presented. The temporal evolution of disturbances during the transient period are compared with the spatial evolution of the same disturbances and a strong correlation between the two approaches is demonstrated indicating that the theory may be used for the transient period of disturbance evolution. The theory and simulations demonstrate that strong amplification of the disturbances can occur as a result of the inclusion of the continuum in the prediction of disturbance evolution. The results further show that any approach proposed for use in bypass boundary layer transition must include the transient growth that results from the continuum. Finally, although a connection between temporal and spatial evolution in the transient period has been demonstrated, a theoretical basis as an explanation for this connection remains the focus of additional study.