Streamwise Algebraic Growth (and Breakdown) in Three-Dimensional Boundary Layers

We investigate the effect of flow perturbations on a broad class of three-dimensional boundary-layer flows applicable close to lines of symmetry. The base-flow class includes all the classical two-dimensional Falkner–Skan solution family, together with a three-dimensional solution family involving a crossflow velocity component. When considering perturbations to these flows (which take on the same crossflow form as the base states), linear, steady eigenstates which grow algebraically in the streamwise direction frequently exist (including in the case of Blasius flow). The natural question that arises is whether nonlinear effects can in turn provoke a transition process; this is the main focus of this paper. The methodology is fully rational, with, in particular, non-parallel effects being treated in an entirely proper manner. In the case of steady flow perturbations, two scenarios are found to occur in our numerical results: either the nonlinear response arising from the growth of linear eigenstates leads to a translation from one solution branch to another (one not possessing steady, linear, leading-edge eigenstates), or alternatively a nonlinear breakdown/singularity occurs at a finite downstream location, which may be interpreted physically as a burst of vorticity out of the boundary layer, linked to an early phase of the transition process. In the case of temporally periodic disturbances, these always lead to a breakdown; however, temporally impulsive-type disturbances lead to a wave-packet-like response downstream, which may or may not ultimately breakdown. Received 10 December 2001 and accepted 1 October 2002 Published online 5 February 2003 Communicated by P. Hall