Abstract
A formal solution to the initial value problem for a plane vortex sheet in an inviscid fluid is obtained by transform methods. The eigenvalue problem is investigated and the stability criterion determined. This criterion is found to be in agreement with that obtained previously by Landau (1944), Hatanaka (1949), and Pai (1954), all of whom had included spurious eigenvalues in their analyses. It is also established that supersonic disturbances may be unstable; related investigations in hydrodynamic stability have conjectured on this possibility, but the vortex sheet appears to afford the first definite example. Finally, an asymptotic approximation is developed for the displacement of a vortex sheet following a suddenly imposed, spatially periodic velocity.
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