{"paper":{"title":"Eroding dipoles and vorticity growth for Euler flows in $ \\scriptstyle{\\mathbb{R}}^3$ I. Axisymmetric flow without swirl","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Andrew D. Gilbert, Paul Valiant, Stephen Childress","submitted_at":"2015-12-24T20:31:45Z","abstract_excerpt":"A review of analyses based upon anti-parallel vortex structures suggests that structurally stable vortex structures with eroding circulation may offer a path to the study of rapid vorticity growth in solutions of Euler's equations in $ \\scriptstyle{\\mathbb{R}}^3$. We examine here the possible formation of such a structure in axisymmetric flow without swirl, leading to maximal growth of vorticity as $t^{4/3}$. Our study suggests that the optimizing flow giving the $t^{4/3}$ growth mimics an exact solution of Euler's equations representing an eroding toroidal vortex dipole which locally conserve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07898","kind":"arxiv","version":1},"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"}