{"paper":{"title":"The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.ao-ph"],"primary_cat":"nlin.CD","authors_text":"D. D. Holm, J. D. Gibbon","submitted_at":"2010-06-19T20:56:45Z","abstract_excerpt":"The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity $\\bdB = \\bnabla q\\times \\bnabla\\theta$ for the three-dimensional incompressible rotating Euler equations evolves according to the same stretching equation as for $\\bom$ the vorticity and $\\bB$, the magnetic field in magnetohydrodynamics (MHD). The $\\bdB$-vector therefore acts like the vorticity $\\bom$ in Euler's equations and the $\\bB$-field in MHD. For example, it al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3891","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"}