{"paper":{"title":"Bounding the scalar dissipation scale for mixing flows in the presence of sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Alexandra Tzella, Alexandros Alexakis","submitted_at":"2011-03-25T16:15:15Z","abstract_excerpt":"We investigate the mixing properties of scalars stirred by spatially smooth, divergence-free flows and maintained by a steady source-sink distribution. We focus on the spatial variation of the scalar field, described by the {\\it dissipation wavenumber}, $k_d$, that we define as a function of the mean variance of the scalar and its gradient. We derive a set of upper bounds that for large P\\'eclet number ($\\Pe\\gg1$) yield four distinct regimes for the scaling behavior of $k_d$, one of which corresponds to the Batchelor regime. The transition between these regimes is controlled by the value of $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5011","kind":"arxiv","version":2},"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"}