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At large Reynolds number $Nu Pr^{1/3}$ and $Re Pr$ are function only of $Ra Pr^{2/3}$ (within logarithmic corrections). In practice, since $Nu$ is always close to $Ra^{1/3}$, this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Rey"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.1548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-06-08T12:23:07Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"0d86d8153138b5e4dee0424894b7619e923c3fa515585996df24de8cac401043","abstract_canon_sha256":"ef7e9856cb56a139a64005f94d89b9366fc199dbef1601ec10ca9ca08886cd5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:40.856729Z","signature_b64":"0GFEy0psvZa2PybHfBR6syQb0Z+C3Qcs/ePjETfKEAB26dXd3EP0MQb+WQ1iWehbmtOfoOU9g9F52RIzRxy9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e73b079d32013a7a2e00f6ba4d1be2577e9284eb09dd878b8c6e8c5e8b46170","last_reissued_at":"2026-05-18T02:01:40.856217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:40.856217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling in large Prandtl number turbulent thermal convection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"nlin.CD","authors_text":"B. 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