Data for paper "Singularity formation of vortex sheets in two-dimensional Euler equations using the characteristic mapping method"

This repository contains the data for the paper:

Title: Singularity formation of vortex sheets in two-dimensional Euler equations using the characteristic mapping methodAuthors: Julius Bergmann, Thibault Maurel-Oujia, Xi-Yuan Yin, Jean-Christophe Nave, Kai SchneiderAbstract: The goal of this numerical study is to gain insight into singular solutions of the two-dimensional (2D) Euler equations for nonsmooth initial data, particularly vortex sheets. High-resolution computations of vortex layers in two-dimensional incompressible Euler flows are performed using the characteristic mapping method (CMM), a semi-Lagrangian approach that evolves the flow map with the gradient-augmented level set method. The semigroup structure of the flow map allows decomposition into submaps over finite time intervals, enabling precision control through appropriate remapping times. By composing the flow map, CMM achieves exponential resolution in linear time, uniquely resolving fine-scale flow structures in great detail. This study examines the roll-up process of vortex layers, varying their thickness to analyze its impact on palinstrophy growth and the potential blow-up of absolute vorticity. The curvature of the vortex sheet exhibits singular-like behavior, and the self-similar structure of the vortex core is explored in the vanishing thickness limit. By tracking singularities in the complex plane, conclusions are drawn about the potential presence of singularities in the two-dimensional Euler equations for nonsmooth initial data.URL: https://doi.org/10.1063/5.0241214

For the vortex sheet initial condition, data for simulations with 5 different sheet thicknesses are presented. The data contains metadata information, particle data of the center line and flow data for the vorticity and gradient of the vorticity for constructing the palinstrophy. The data is in binary form (IEEE double precision), more information on the file structure can be taken from the repository of the code software.

The source code of the CMM-Cuda-Code can be found here: https://github.com/CharacteristicMappingMethod/cmm-turbulence