{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4RI5T7AEJOFT56NA7LV6Z2TNCB","short_pith_number":"pith:4RI5T7AE","schema_version":"1.0","canonical_sha256":"e451d9fc044b8b3ef9a0faebecea6d105e72128ee19234a6d948dba83367e90d","source":{"kind":"arxiv","id":"1109.6870","version":1},"attestation_state":"computed","paper":{"title":"Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Detlef Lohse, Olga Shishkina, Richard J. A. M. Stevens, Siegfried Grossmann","submitted_at":"2011-09-30T15:58:50Z","abstract_excerpt":"Results on the Prandtl-Blasius type kinetic and thermal boundary layer thicknesses in turbulent Rayleigh-B\\'enard convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary layer equations, we calculate the ratio of the thermal and kinetic boundary layer thicknesses, which depends on the Prandtl number Pr only. It is approximated as $0.588Pr^{-1/2}$ for $Pr\\ll Pr^*$ and as $0.982 Pr^{-1/3}$ for $Pr^*\\ll\\Pr$, with $Pr^*= 0.046$. Comparison of the Prandtl--Blasius velocity boundary layer thickness with that evaluated in the direct numerical simu"},"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":"1109.6870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2011-09-30T15:58:50Z","cross_cats_sorted":[],"title_canon_sha256":"acc73e1eeeb3b4df585535f412ed3088cf439459f59895d2bbd8e10098ad6d71","abstract_canon_sha256":"ca33273e76782cab7c27b076ca6ef024fa779bd457190d66065dee2ccfddabc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:35.862878Z","signature_b64":"+696CsyhrZoA7+dIAjlsEogd/I146wO3bSA3WdkF1mJapQDJDt7Rjk1fM9Djkuh5qkcC4XdHdONbydl1xN3zCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e451d9fc044b8b3ef9a0faebecea6d105e72128ee19234a6d948dba83367e90d","last_reissued_at":"2026-05-18T02:21:35.862443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:35.862443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Detlef Lohse, Olga Shishkina, Richard J. A. M. Stevens, Siegfried Grossmann","submitted_at":"2011-09-30T15:58:50Z","abstract_excerpt":"Results on the Prandtl-Blasius type kinetic and thermal boundary layer thicknesses in turbulent Rayleigh-B\\'enard convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary layer equations, we calculate the ratio of the thermal and kinetic boundary layer thicknesses, which depends on the Prandtl number Pr only. It is approximated as $0.588Pr^{-1/2}$ for $Pr\\ll Pr^*$ and as $0.982 Pr^{-1/3}$ for $Pr^*\\ll\\Pr$, with $Pr^*= 0.046$. Comparison of the Prandtl--Blasius velocity boundary layer thickness with that evaluated in the direct numerical simu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6870","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.6870","created_at":"2026-05-18T02:21:35.862506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.6870v1","created_at":"2026-05-18T02:21:35.862506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6870","created_at":"2026-05-18T02:21:35.862506+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RI5T7AEJOFT","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RI5T7AEJOFT56NA","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RI5T7AE","created_at":"2026-05-18T12:26:20.644004+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/4RI5T7AEJOFT56NA7LV6Z2TNCB","json":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB.json","graph_json":"https://pith.science/api/pith-number/4RI5T7AEJOFT56NA7LV6Z2TNCB/graph.json","events_json":"https://pith.science/api/pith-number/4RI5T7AEJOFT56NA7LV6Z2TNCB/events.json","paper":"https://pith.science/paper/4RI5T7AE"},"agent_actions":{"view_html":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB","download_json":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB.json","view_paper":"https://pith.science/paper/4RI5T7AE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.6870&json=true","fetch_graph":"https://pith.science/api/pith-number/4RI5T7AEJOFT56NA7LV6Z2TNCB/graph.json","fetch_events":"https://pith.science/api/pith-number/4RI5T7AEJOFT56NA7LV6Z2TNCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB/action/storage_attestation","attest_author":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB/action/author_attestation","sign_citation":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB/action/citation_signature","submit_replication":"https://pith.science/pith/4RI5T7AEJOFT56NA7LV6Z2TNCB/action/replication_record"}},"created_at":"2026-05-18T02:21:35.862506+00:00","updated_at":"2026-05-18T02:21:35.862506+00:00"}