Spatiotemporal growing wave fronts in spatially stable boundary layers

In fluid dynamical systems, it is not known a priori whether disturbances grow either in space or in time or as spatiotemporal structures. For a zero pressure gradient boundary layer (also known as the Blasius boundary layer), it is customary to treat it as a spatial problem, and some limited comparison between prediction and laboratory experiments exist. In the present work, the two-dimensional receptivity problem of a Blasius boundary layer excited by a localized harmonic source is investigated under the general spatiotemporal framework, by using the Bromwich contour integral method. While this approach is seen to be equivalent to the spatial study for unstable systems, here we show for the first time how spatially stable systems show spatiotemporally growing wave fronts.