{"paper":{"title":"Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"nlin.CD","authors_text":"D. D. Holm, J. D. Gibbon","submitted_at":"2010-12-16T13:40:14Z","abstract_excerpt":"Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vorticity ($q = \\bom\\cdot\\nabla\\theta$) associated with solutions of the three-dimensional Euler and Navier-Stokes equations. The vector $\\bdB = \\nabla q \\times \\nabla\\theta$ satisfies the same type of stretching and folding equation as that for the vorticity field $\\bom $ in the incompressible Euler equations (Gibbon & Holm, 2010). The quantity $\\theta$ may be chosen as the potential temperature for the stratified, rotating Euler/Navier-Stokes equations, or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3597","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"}