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arXiv · 1210.1981

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

Stephen Childress
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Abstract

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 local 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.

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Stephen Childress. 2012-10-06. A model for singularity formation in three-dimensional Euler and Navier-Stokes flows. https://arxiv.org/abs/1210.1981

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