High resolution vortex layer computations in 2D Euler flows using a characteristic mapping method*

The goal of this study is to get insight into singular solutions of the 2D Euler equations for non-smooth initial data, in particular for vortex sheets. To this end high resolution computations of vortex layers in 2D incompressible Euler flows are performed using the characteristic mapping method. This semi-Lagrangian flow method evolves the flow map using the gradient-augmented level set method (GALSM). The semi-group structure of the flow map allows its decomposition into submaps (each over a finite time interval), and thus the error can be controlled by choosing appropriate remapping times. It yields exponential resolution in linear time and fine scale flow structures are resolved which can be analyzed in detail. Here the roll-up process of vortex layers is studied varying the thickness of the layer showing its impact on the growth of palinstrophy. The self-similar structure of the vortex core is investigated in the vanishing thickness limit. Conclusions on the non-uniqueness of weak solutions of 2D Euler for non-smooth initial data will be drawn and the presence of flow singularities is revealed.