2012/10/06 by Stephen Childress, Childress, Stephen
Chemical Engineering · Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Mathematical Physics (math-ph) #Rheology and Fluid Dynamics Studies #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1210.1981
Withdrawn for major revision and correction of conclusions for Navier-Stokes flows
openalex publication_date 2012/10/06 · arxiv created 2012/10/26 · arxiv updated 2012/10/29 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
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.