The final approach to steady state in an axisymmetric stagnation flow following a change in free stream velocity

Analytical consideration is given to the development of steady flow in the viscous region of the boundary layer of an incompressible fluid near the axisymmetric stagnation point. Governing equations are defined for mass and momentum, and boundary conditions are configured for a flow around a circular cylinder. A formulation is developed for solving for a perturbation from the steady state. The differential of the perturbation is demonstrated to have a smooth exponential decay at infinity, and to have nonzero unsteady behavior between its end points. Finally, an analytical model for the velocity field is obtained.