Do vortex sheets roll up?

We discuss the evolution of a spatially periodic, perturbed vortex sheet following the formation of a curvature singularity at a critical time as demonstrated by Moore (Proc. R. Soc. A, 1979). Vortex-sheet regularization is not used. We first extend the Moore analysis to give the sheet shape and strength over a full wavelength at the critical time. This provides a singular initial condition defining a sheet evolution for times beyond singularity formation for which the most singular term in the defining Birkhoff-Rott (BR) equation is obtained from a Taylor-series expansion. The series can be summed analytically providing a closed-form solution in an intermediate region defined by a similarity variable proportional to circulation/time and time itself. An inner-region, vortex-sheet evolution is found based on an expansion of the BR equation in powers of the square-root of time with coefficients as functions of the similarity variable defined by both non-linear and linear similarity equations. Numerical solutions are found which match the intermediate-region solutions. The composite structure elucidates the long-standing question of vortex-sheet roll up following singularity formation.