Journal of Fluid Mechanics

Similarity solutions of the two-dimensional unsteady boundary-layer equations

Philip K. H.  Ma a1 and W. H.  Hui a1
a1 University of Waterloo, Waterloo, Ontario, Canada. N2L 3G1

Article author query
ma pk   [Google Scholar] 
hui wh   [Google Scholar] 


The method of Lie group transformations is used to derive all group-invariant similarity solutions of the unsteady two-dimensional laminar boundary-layer equations. A new method of nonlinear superposition is then used to generate further similarity solutions from a group-invariant solution. Our results are shown to include all the existing solutions as special cases. A detailed analysis is given to several classes of solutions which are also solutions to the full Navier–Stokes equations and which exhibit flow separation.

(Published Online April 26 2006)
(Received August 16 1989)