The equation governing the evolution of a vortex layer whose thickness is small compared to its radius of curvature and in which the vorticity is everywhere the same is obtained, viscous and compressibility effects being neglected. The method of matched asymptotic expansions is applied and results in an extension, which is unexpectedly simple, of Birkhoff's integro‐differential equation for vortex sheets. The equation is applied to long waves on a straight vortex layer of uniform thickness.
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Dennis W. Moore (1978) studied this question.
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