New similarity solutions of the unsteady incompressible boundary-layer equations

The standard boundary-layer equations play a central role in many aspects of fluid mechanics as they describe the motion of a slightly viscous fluid close 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 demonstrate the existence of reductions which take the boundary-layer forms to lower-order partial differential systems and others which simplify them to 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 some completely new forms.