###
The question of finite time singularities in the Euler and Navier-Stokes equation
is one of the outstanding open problems in fluid dynamics with strong implications
on the intermittency properties of turbulent flows. The mathematical question
whether smooth initial condition
stay smooth for all times or develop singularities
in finite time was recognized as one of the Millenium problems by the
Clay Mathematics Institute. We try to gain further insight into
this problem by performing high resolution adaptive mesh refinement simulations
using our new developed framework racoon for massive parallel computations. Recent
mathematical theorems highlight the importance of the geometry (curvature) of vortex lines
and the divergence of the direction of vortex lines in a vortex tube near the possible
singularity. In order to testify the mathematical assumptions of theorems which provide
necessary conditions for the existence of global solutions, we advect passive tracer
particles with the flow to follow the dynamics of the vortex lines and their geometric properties.

## Principal Investigators:

### Prof. Dr. R. Grauer

Institute for Theoretical Physics I

Ruhr-University Bochum

### Dr. Jürgen Dreher

Institute for Theoretical Physics I

Ruhr-University Bochum

## PhD Students

### Tobias Grafke

Institute for Theoretical Physics I

Ruhr-University Bochum

### Thorsten Hater

Institute for Theoretical Physics I

Ruhr-University Bochum)