{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WB2LFEUQ2OG7NEL4IILG7SLHMK","short_pith_number":"pith:WB2LFEUQ","schema_version":"1.0","canonical_sha256":"b074b29290d38df6917c42166fc96762a91f6973a79ad3e9b8e551228a8dd639","source":{"kind":"arxiv","id":"1511.00989","version":2},"attestation_state":"computed","paper":{"title":"On the emergence of the Navier-Stokes-$\\alpha$ model for turbulent channel flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bingsheng Zhang, Ciprian Foias, Jing Tian","submitted_at":"2015-10-31T21:34:56Z","abstract_excerpt":"In a series of papers (see \\cite{CDT02} and the pertinent references therein) the 3D Navier-Stokes-$\\alpha$ model were shown to be a useful complement to the 3D Navier-Stokes equations; and in particular, to be a good Reynolds version of the latter equations. In this work, we introduce a simple Reynolds averaging which, due to the wall roughness, transforms the Navier-Stokes equations into the Navier-Stokes-$\\alpha$ model."},"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":"1511.00989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-31T21:34:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"914861caed600dbad68be03d58dd785b1148e12a12125fd2214d8c8e539ba305","abstract_canon_sha256":"23a1b4035a1bdb8219fc310c695058d9de1cc8e3ed6cb352be1a190ec02a6253"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:22.224020Z","signature_b64":"UixGIBYEorAqKE3BDT5uJGHAWLJXJY7RdxROqjEcRnqNb/B3Xs+/2sxx+lOGnfx97O/e0Ia6j5v+HpGYCsWNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b074b29290d38df6917c42166fc96762a91f6973a79ad3e9b8e551228a8dd639","last_reissued_at":"2026-05-18T01:04:22.223374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:22.223374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the emergence of the Navier-Stokes-$\\alpha$ model for turbulent channel flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bingsheng Zhang, Ciprian Foias, Jing Tian","submitted_at":"2015-10-31T21:34:56Z","abstract_excerpt":"In a series of papers (see \\cite{CDT02} and the pertinent references therein) the 3D Navier-Stokes-$\\alpha$ model were shown to be a useful complement to the 3D Navier-Stokes equations; and in particular, to be a good Reynolds version of the latter equations. In this work, we introduce a simple Reynolds averaging which, due to the wall roughness, transforms the Navier-Stokes equations into the Navier-Stokes-$\\alpha$ model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00989","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":"1511.00989","created_at":"2026-05-18T01:04:22.223476+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00989v2","created_at":"2026-05-18T01:04:22.223476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00989","created_at":"2026-05-18T01:04:22.223476+00:00"},{"alias_kind":"pith_short_12","alias_value":"WB2LFEUQ2OG7","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WB2LFEUQ2OG7NEL4","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WB2LFEUQ","created_at":"2026-05-18T12:29:47.479230+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/WB2LFEUQ2OG7NEL4IILG7SLHMK","json":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK.json","graph_json":"https://pith.science/api/pith-number/WB2LFEUQ2OG7NEL4IILG7SLHMK/graph.json","events_json":"https://pith.science/api/pith-number/WB2LFEUQ2OG7NEL4IILG7SLHMK/events.json","paper":"https://pith.science/paper/WB2LFEUQ"},"agent_actions":{"view_html":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK","download_json":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK.json","view_paper":"https://pith.science/paper/WB2LFEUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00989&json=true","fetch_graph":"https://pith.science/api/pith-number/WB2LFEUQ2OG7NEL4IILG7SLHMK/graph.json","fetch_events":"https://pith.science/api/pith-number/WB2LFEUQ2OG7NEL4IILG7SLHMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK/action/storage_attestation","attest_author":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK/action/author_attestation","sign_citation":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK/action/citation_signature","submit_replication":"https://pith.science/pith/WB2LFEUQ2OG7NEL4IILG7SLHMK/action/replication_record"}},"created_at":"2026-05-18T01:04:22.223476+00:00","updated_at":"2026-05-18T01:04:22.223476+00:00"}