3D Euler about a 2D symmetry plane

Initial results from new calculations of interacting anti-parallel Euler vortices are presented with the objective of understanding the origins of singular scaling presented by Kerr [R.M. Kerr, Evidence for a singularity of the three-dimensional, incompressible Euler equations, Phys. Fluids 5 (1993) 1725–1746] and the lack thereof by Hou and Li [T.Y. Hou, R. Li, Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations, J. Nonlinear Sci. 16 (2006) 639–664]. Core profiles designed to reproduce the two results are presented, new more robust analysis is proposed, and new criteria for when calculations should be terminated are introduced and compared with classical resolution studies and spectral convergence tests. Most of the analysis is on a 512×128×2048 mesh, with new analysis on a just completed 1024×256×2048 used to confirm trends. One might hypothesize that there is a finite-time singularity with enstrophy growth like Ω ∼ (Tc − t)−γΩ and vorticity growth like ‖ω‖∞ ∼ (Tc − t)−γ . The new analysis would then support γΩ ≈ 1/2 and γ > 1. These represent modifications of the conclusions of Kerr [op. cit.]. Issues that might arise at higher resolution are discussed. c © 2008 Elsevier B.V. All rights reserved. PACS: 47.10.A-; 47.11.Kb; 47.15.ki