Boundary-layer flow along a ridge: alternatives to the Falkner-Skan solutions

We consider the laminar boundary-layer flow past a semi-infinite plate with a streamwise ridge. We seek similarity solutions to the problem, when the freestream velocity takes the form x*n, where x* denotes the distance from the leading edge of the plate; such solutions may exist if the transverse a nd lateral scales of the ridge develop in the streamwise direction at the s ame rate as the boundary-layer thickness grows. In deriving the necessary f ar-field boundary conditions for these calculations, we are led to a consid eration of a class of flows of the Falkner-Skan type, but which may possess a cross-flow component of velocity (which grows linearly in the cross-flow direction). This new class of how is a three-dimensional alternative to th e Falkner-Skan family. Wall transpiration effects are also addressed and po rtions of the solution curves correspond to separated flows. Solutions for the flow along a ridge for both the aforementioned classes of far-field beh aviour are presented. A study of the effects of relaxing the similarity constraint on both the cl assical solution and new families of solution is also made. It is found tha t the problem is (frequently) complicated by the existence of spatially dev eloping eigensolutions (originating from the leading edge), which have the effect of rendering standard parabolic marching procedures ill posed.