Mathematics Colloquia and Seminars

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A vortex sheet is a model for a shear flow which represents a thin layer of vorticity by a surface of zero thickness in inviscid flow. Under the governing Euler Equations the vortex sheets generically develop singularities in finite time. With the goal of approximating the shear flows past singularity formation the govering equations are regularized. Various regularizations are possible. In this talk I will discuss two issues that arise in vortex sheet computations. The first regards the onset of irregular chaotic motion in the regularized flow. I will present results using various regularizations and discuss open questions about the dependence of the behaviour on the regularization. The second issue regards large errors introduced in axisymmetric unregularized computations due to the singularity of the axisymmetric coordinate system on the axis. I will describe the errors and their origins, and present a method to resolve them.