Unsteady Axisymmetric Stagnation Flow on a Circular Cylinder

Unsteady, axisymmetric stagnation flow about a circular cylinder is examined when the far-field flow is a periodic function of time with a fixed time average and an oscillatory part of prescribed amplitude and frequency. Solutions are computed for arbitrary values of the Reynolds number, quantifying the effects of surface curvature, and a frequency parameter based on the period of the far-field flow. It is found that solutions remain regular and periodic provided that the far-field amplitude lies below a critical value. Above this value, solutions terminate in a finite-time singularity. The blow-up time is delayed by increasing the curvature of the surface. These results are corroborated by asymptotic predictions valid in the limits of small and large amplitude and frequency. For large Reynolds number, the problem reduces to the two-dimensional stagnation-point flow against a plane wall studied by previous authors.