{"paper":{"title":"Eroding dipoles and vorticity growth for Euler flows in $ \\scriptstyle{\\mathbb{R}}^3$: The hairpin geometry as a model for finite-time blowup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Andrew D. Gilbert, Stephen Childress","submitted_at":"2016-12-22T17:18:51Z","abstract_excerpt":"A theory of an eroding \"hairpin\" vortex dipole structure in three dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The hairpin is here similarly proposed as a model to produce large \"self-stretching\" of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of \"generalized\" form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07709","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}