{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"901d4beb922ba9765caaba173508d8cb545183cd9ad8f0e984fb0832f7f4d4c2","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","70b03dbd933ef88fa9a98dc1f0036ecb69609888555d805ef03d9f8956caae39"],"salt":"5155822ac40b62f835b3428cd823a52bf342f48e34d1db2a33a6874f92fec659","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"fluid.small-scale.exponent-saturation","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[{"note":"","parent_revision":"70b03dbd933ef88fa9a98dc1f0036ecb69609888555d805ef03d9f8956caae39","relation":"special_case"}],"plain":"The statistics of the most extreme velocity differences appear to stop becoming more extreme beyond a certain order, as if the flow had a limiting roughness. Whether this saturation is real, and the same for differences measured along and across the separation, is not established.","posed_since":"","precise":"In isotropic Navier-Stokes turbulence at $\\mathrm{Re}_{\\lambda} \\to \\infty$, do the transverse and longitudinal exponents $\\zeta_p^T$ and $\\zeta_p^L$ tend to a common finite limit $\\zeta_{\\mathrm{inf}}$ as $p \\to \\infty$? DNS up to $\\mathrm{Re}_{\\lambda} \\sim 1300$ report saturation of transverse exponents near $\\zeta_{\\mathrm{inf}} \\sim 2$. Answer: yes or no for each increment type, with $\\zeta_{\\mathrm{inf}}$ and error bars from statistically converged tails for $p$ up to about 12.","problem_ref":null,"references":"","settled_by":"Converged DNS or experimental moments of both increment types at $Re_{\\lambda}$ above about 2000 showing a common plateau, or a demonstrated difference.","status_note":"Transverse saturation near 2 in isotropic DNS (Iyer, Sreenivasan, Yeung 2020); longitudinal saturation near $2.2 \\pm 0.1$ in turbulent shear layers at $\\operatorname{Re}_{\\lambda}$ up to 1400 (Gupta and Bewley 2026, arXiv:2605.01867); whether the two limits coincide in isotropic turbulence is untested.","title":"Do high-order structure-function exponents saturate at large order?","topic_ref":"45474d2178078204b5f1dbc4ca64d4b74ada936d74d13eddb4d83cc4b1e3c985"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b89ed7f03ad15b8586ce0c2661e0e62ba903936375fb063a951aeeb0b3c5a071","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"ebfd8d75efdc46816b7a4fd4bc5707d4fff46f3939d6f44e6c6c6ce0aed08421","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"OgR61RRSF-urQoWwybBkXVYuLgrAM3ZrIy5ZNCa5jxFGWKmMCX7YDW4bMRwLEw3V1WsziZlw8BeNw-pdaJLvBw"},"schema":"pubphys.envelope/1"},"record_hash":"b89ed7f03ad15b8586ce0c2661e0e62ba903936375fb063a951aeeb0b3c5a071","leaf_index":1435}