1210.1981 (Stephen Childress)

A model for singularity formation in three-dimensional Euler and
Navier-Stokes flows    [PDF]

Stephen Childress

We present a formal, approximate model for singularity formation in classical fluid dynamics in three dimensions. The construction utilizes an approximation of local two-dimensionality to study an anti-parallel hairpin vortex structure with a cross-section equivalent to the 2D Chaplygin-Lamb dipole vortex. The model exhibits a finite time Euler singularity at an isolated point, with only finite stretching of vortex lines. The model also suggests an associated Navier-Stokes problem, which exhibits a finite-time point singularity, provided that a Reynolds number is sufficiently large. The singularities are compatible with both the BKM [1] and CF[2] conditions. The vorticity support is infinite in volume but the singularity forms as a result of local processes requiring only finite energy input.

View original: http://arxiv.org/abs/1210.1981