The Limit of High Reynolds Number for Shear Layers

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8903484 Baker The principal investigator will study the limit at high Reynolds number of shear layers in incompressible fluid using three different methods--vortex methods, spectral methods, and finite difference methods. Classically, the limit is thought to be a vortex sheet, but recent studies suggest that vortex sheets develop curvature singularities in finite time, and that at the time of singularity formation, the vortex sheet changes from a weak solution to a measure-valued solution of Euler equations. Moreover, different regularizations may lead to different results, making the nature of the limit of vanishing viscosity a central concern. The different numerical methods are considered in order to obtain a direct check on the accuracy of the results, to make a direct comparison of the performance of these methods on shear flows and to identify areas for improvement in each method. Results of the numerical calculations will be used to study how viscous effects modify the tendency for vortex sheets to develop curvature singularities. Numerical results will also be used to help answer the open mathematical question: do different regularizations of the Euler equations converge to different limits as the regularization vanishes?