{"paper":{"title":"Dissipation statistics of a passive scalar in a multidimensional smooth flow","license":"","headline":"","cross_cats":["cond-mat.stat-mech","nlin.CD"],"primary_cat":"chao-dyn","authors_text":"A. Gamba, I. V. Kolokolov","submitted_at":"1998-07-31T17:43:26Z","abstract_excerpt":"We compute analytically the probability distribution function ${\\cal P}(\\epsilon)$ of the dissipation field $\\epsilon =(\\nabla \\theta)^{2}$ of a passive scalar $\\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime). The tail of the distribution is a stretched exponential: for $\\epsilon \\to \\infty$, $\\ln {\\cal P}(\\epsilon)\\sim -(d^2\\epsilon)^{1/3}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9808001","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"}