The boundary layer created by the motion of a single rectilinear vortex filament above an infinite plane wall is considered. In a frame of reference which moves uniformly with the vortex the inviscid motion is steady; however, the possibility of a corresponding steady boundary-layer solution can be ruled out and it is concluded that the boundary-layer flow is inherently unsteady for all time. To investigate the nature of the unsteady boundary-layer flow, a time-dependent problem, corresponding to the sudden insertion of the plane wall at time $t$ = 0, is considered; separation in the boundary layer is found to take place in a short period of time and the solution shows possibly explosive features as $t$ increases. It is conjectured that an eventual eruption of the boundary-layer flow is to be expected along with a major modification of the inviscid flow. The theory compares favourably with experiments on the flow induced near the ground by trailing aircraft vortices.