{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HHOL36P2CABV3UDX2HKTCFLEAD","short_pith_number":"pith:HHOL36P2","schema_version":"1.0","canonical_sha256":"39dcbdf9fa10035dd077d1d531156400c20a6029fd721b50a30974954d94ea79","source":{"kind":"arxiv","id":"1103.3789","version":2},"attestation_state":"computed","paper":{"title":"Field correlations and the ultimate regime of turbulent convection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.SR","nlin.CD"],"primary_cat":"physics.flu-dyn","authors_text":"Ambrish Pandey, Mahendra K. Verma, Pankaj K. Mishra, Supriyo Paul","submitted_at":"2011-03-19T15:21:29Z","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"},"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":"1103.3789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-03-19T15:21:29Z","cross_cats_sorted":["astro-ph.SR","nlin.CD"],"title_canon_sha256":"0238a2182269ed42e87bc49460c6b584e97f0015595418bac2eca190521a4685","abstract_canon_sha256":"a047937bdbb54609a5b07eee8ef7c2bb173c439591ea4887e521681f3cf8f0f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:17.087782Z","signature_b64":"KT1qoDubYTLT/E1XdgBSkp9rk/A+WgoHfNd3TTfy+41cs/tjU0U3vEnwVBGuGS+A1yk6KxpCwVLl5eA6A8+sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39dcbdf9fa10035dd077d1d531156400c20a6029fd721b50a30974954d94ea79","last_reissued_at":"2026-05-18T04:04:17.086875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:17.086875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Field correlations and the ultimate regime of turbulent convection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.SR","nlin.CD"],"primary_cat":"physics.flu-dyn","authors_text":"Ambrish Pandey, Mahendra K. Verma, Pankaj K. Mishra, Supriyo Paul","submitted_at":"2011-03-19T15:21:29Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3789","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.3789","created_at":"2026-05-18T04:04:17.087035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.3789v2","created_at":"2026-05-18T04:04:17.087035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3789","created_at":"2026-05-18T04:04:17.087035+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHOL36P2CABV","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHOL36P2CABV3UDX","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHOL36P2","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD","json":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD.json","graph_json":"https://pith.science/api/pith-number/HHOL36P2CABV3UDX2HKTCFLEAD/graph.json","events_json":"https://pith.science/api/pith-number/HHOL36P2CABV3UDX2HKTCFLEAD/events.json","paper":"https://pith.science/paper/HHOL36P2"},"agent_actions":{"view_html":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD","download_json":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD.json","view_paper":"https://pith.science/paper/HHOL36P2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.3789&json=true","fetch_graph":"https://pith.science/api/pith-number/HHOL36P2CABV3UDX2HKTCFLEAD/graph.json","fetch_events":"https://pith.science/api/pith-number/HHOL36P2CABV3UDX2HKTCFLEAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD/action/storage_attestation","attest_author":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD/action/author_attestation","sign_citation":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD/action/citation_signature","submit_replication":"https://pith.science/pith/HHOL36P2CABV3UDX2HKTCFLEAD/action/replication_record"}},"created_at":"2026-05-18T04:04:17.087035+00:00","updated_at":"2026-05-18T04:04:17.087035+00:00"}