Note on the Instability of a Vortex Sheet Leaving a Semi-Infinite Plate

摘要

The results pertaining to the inviscid instability of a vortex sheet leaving a semi-infinite plate derived by Orszag and Crow (1970) and by Bechert and Michel (1975) were examined. While the former find a solution of the problem which, however, does not satisfy the full Kutta condition, the latter stated that without excitation by sources only the trivial solution exists. It is found that both methods agree completely, but that the no-Kutta-condition solution of Orszag and Crow, in the sense of Bechert and Michel, reflects the existence of a vortex sheet excited by a special dipole sheet along the plate. It is shown that for vortex sheet problems the use of the pressure instead of the velocity potential is more convenient. It is proved that the Wiener-Hopf equation of the present problem corresponds to the differential equation for the vortex sheet displacement derived by Bechert and Michel.