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Stability analysis of boundary layer flow due to the presence of a small hole on a surface.

A linear, temporal, and viscous stability analysis of the boundary layer induced on a solid plane by a three-dimensional potential sink flow is considered. The flow is inviscidly (neutrally) stable. For axisymmetric perturbations, one can analyze separately the stability of those perturbations with a purely circumferential motion, and those with no azimuthal velocity. The first ones are shown to be always stable, a result that is found analytically. The second ones become unstable in a range of (high) Reynolds numbers that depends on the radial wave number. Finally, it is shown that all nonaxisymmetric perturbations are linearly stable.