The critical separation reynolds number for streaming flow past a circular cylinder

Employing a complex variable approach to the equations of motion for an incompressible viscous fluid and a more general approximation to the convecting stream function it is possible to calculate an approximation to the vorticity on the boundary for streaming flow past a circular cylinder without solving first for the complete flow field. In particular it is found that separation at the rear stagnation point first occurs when $\text{R1 = 2.78}$, where $\text{R1}$ is the critical Reynolds number. This result is in good agreement with the value of $\text{R1}$ obtained by experiment and the value obtained numerically. The convecting stream function satisfies the conditions of no slip and vorticity is not convected through the cylinder as it is in small Reynolds number Oseen theory.