The stability of a two-dimensional stagnation flow to three-dimensional disturbances

Experiments have shown that the two-dimensional flow near a forward stagnation line may be unstable to three-dimensional disturbances. The growing disturbance takes the form of secondary vortices, i.e. vortices more or less parallel to the original streamlines. The instability is usually confined to the boundary layer and the spacing of the secondary vortices is of the order of the boundary-layer thickness. This situation is analysed theoretically for the case of infinitesimal disturbances of the type first studied by Görtler and Hämmerlin. These are disturbances periodic in the direction perpendicular to the plane of the flow, in the limit of infinite Reynolds number. It is shown that the flow is always stable to these disturbances.