A series expansion study of the Navier-Stokes equations

An algorithm to derive the relations between the coefficients of a series expansion solution of the incompressible Navier-Stokes and continuity equations is obtained. Steady and unsteady flow are considered. Relations necessary for closure are supplied by the boundary conditions. The algorithm is applied to cases whose solutions were obtained using other methods. The algorithm can be used for computational methods and for generating analytically complex flow patterns which are known to be asymptotic solutions of the Navier-Stokes and continuity equations.