An Asymptotic Matching Condition for Unsteady Boundary-Layer Flows Governed by the Navier-Stokes Equations

It is shown that one condition only, derived from one of Green'sidentities, is necessary to determine the matching of innerand outer expansions in solving problems involving the initialflows of a viscous fluid. This condition has been named an integralcondition, and when it has been satisfied, in the form of aset of conditions for the spectral components, the inner solutionis obtained by a straightforward integration procedure and theouter solution is obtained merely by substituting the innersolution in an integral. Two examples of the method are considered,including that of flow past a suddenly started circular cylinderand flow due to a suddenly started rotating sphere.