New similarity solutions of the unsteady incompressible boundary-layer equations

The standard boundary-layer equations play a central role in many aspects o f fluid mechanics as they describe the motion of a slightly viscous fluid c lose to a surface. A number of exact solutions of these equations have been found and here we extend the class of known solutions by implementing the Clarkson-Kruskal direct method (1) for finding similarity reductions. We de monstrate the existence of reductions which take the boundary-layer forms t o lower-order partial differential systems and others which simplify them t o the solution of ordinary differential equations. It is shown how not only do we recover many of the previously known exact solutions but also find s ome completely new forms.