{"paper":{"title":"The Scalings of Scalar Structure Functions in a Velocity Field with Coherent Vortical Structures","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"J. C. Vassilicos, Md. A. I. Khan","submitted_at":"2000-03-10T13:31:47Z","abstract_excerpt":"In planar turbulence modelled as an isotropic and homogeneous collection of 2-D non-interacting compact vortices, the structure functions S_p(r) of a statistically stationary passive scalar field have the following scaling behaviour in the limit where the P\\'eclet number Pe -> \\infty S_p(r) ~ constant+\\ln({\\frac{r}{LPe^{-1/3}}}) for LPe^{-1/3} << L, S_p(r) ~ ({\\frac{r}{LPe^{-1/3}}})^{6(1-D)} for LPe^{-1/2} << LPe^{-1/3}, where L is a large scale and D is the fractal co-dimension of the spiral scalar structures generated by the vortices (1/2 <= D < 2/3). Note that LPe^{-1/2} is the scalar Taylo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0003027","kind":"arxiv","version":3},"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"}