Boundary layer on a sphere accelerating from rest

The case of a sphere accelerating in a viscous fluid is considered analytically for small time spans, with a system of nonstationary Navier-Stokes equations in curvilinear coordinates yielding a small perturbation problem. Convection effects appear for very small Re as second order terms in the boundary layer terms, and when Re is very large, the convection terms uncouple from the curvature effects. Three regions found close to the stagnation point are described as an outer region where Euler equations apply, an inner region where full boundary layer equations apply, and an inner region where steady Navier-Stokes equations apply. The formulations are found to agree well with previous experimental studies of the trajectory of a sphere.