Abstract
The occurrence of a finite time singularity in the incompressible Euler equations in three dimensions is studied numerically using the technique of adaptive mesh refinement. As opposed to earlier treatments, a prescribed accuracy is guaranteed over the entire integration domain. A singularity in the vorticity could be traced down to five levels of refinement which corresponds to a resolution of mesh points in a nonadaptive treatment. The growth of vorticity fits a power law behavior proportional to where denotes the time when the singularity occurs.
- Received 3 December 1997
DOI:https://doi.org/10.1103/PhysRevLett.80.4177
©1998 American Physical Society