Keywords: vortex sheet motion, vortex blob method, Euler-alpha model Abstract: The vortex sheet is a mathematical model for a shear layer in which the layer is approximated by a surface. Vortex sheet evolution has been shown to approximate the motion of shear layers well, both in the case of free layers and of separated flows at sharp edges. Generally, the evolving sheets develop singularities in finite time. To approximate the fluid past this time, the motion is regularized and the sheet defined as the limit of zero regularization. However, besides weak existence results in special cases, very little is known about this limit. In particular, it is not known whether the limit is unique or whether it depends on the regularization. I will discuss several regularizing mechanisms, including physical ones such as fluid viscosity, and purely numerical ones such as the vortex blob and the Euler-alpha methods. I will show results for a model problem and discuss some of the unanswered questions of interest.