{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HHOL36P2CABV3UDX2HKTCFLEAD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a047937bdbb54609a5b07eee8ef7c2bb173c439591ea4887e521681f3cf8f0f6","cross_cats_sorted":["astro-ph.SR","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-03-19T15:21:29Z","title_canon_sha256":"0238a2182269ed42e87bc49460c6b584e97f0015595418bac2eca190521a4685"},"schema_version":"1.0","source":{"id":"1103.3789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3789","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3789v2","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3789","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"HHOL36P2CABV","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HHOL36P2CABV3UDX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HHOL36P2","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:d7220d309c04b4d4a31685d268e5242bc7242e5e228d789873fcb7530ff1596f","target":"graph","created_at":"2026-05-18T04:04:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Using direct numerical simulations of Rayleigh-B\\'{e}nard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary condit","authors_text":"Ambrish Pandey, Mahendra K. Verma, Pankaj K. Mishra, Supriyo Paul","cross_cats":["astro-ph.SR","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-03-19T15:21:29Z","title":"Field correlations and the ultimate regime of turbulent convection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3789","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e4fe2bbf2dc2953df29154830b68112b6e8b77f9d2d5a6673cc7d17268471b9e","target":"record","created_at":"2026-05-18T04:04:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a047937bdbb54609a5b07eee8ef7c2bb173c439591ea4887e521681f3cf8f0f6","cross_cats_sorted":["astro-ph.SR","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-03-19T15:21:29Z","title_canon_sha256":"0238a2182269ed42e87bc49460c6b584e97f0015595418bac2eca190521a4685"},"schema_version":"1.0","source":{"id":"1103.3789","kind":"arxiv","version":2}},"canonical_sha256":"39dcbdf9fa10035dd077d1d531156400c20a6029fd721b50a30974954d94ea79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39dcbdf9fa10035dd077d1d531156400c20a6029fd721b50a30974954d94ea79","first_computed_at":"2026-05-18T04:04:17.086875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.086875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KT1qoDubYTLT/E1XdgBSkp9rk/A+WgoHfNd3TTfy+41cs/tjU0U3vEnwVBGuGS+A1yk6KxpCwVLl5eA6A8+sCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.087782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4fe2bbf2dc2953df29154830b68112b6e8b77f9d2d5a6673cc7d17268471b9e","sha256:d7220d309c04b4d4a31685d268e5242bc7242e5e228d789873fcb7530ff1596f"],"state_sha256":"6bd5188b92cb8d842b3373b82131701f10d914af2c2bfa971fd49a4b25222c81"}