{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"2260d994e1d238f004cd7d8d693777436bb9f2a2748bbab0f543fc713366b7d1","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"fe6df4abf7dde7f30834ee171e5053145544312d2c7e6e63b2209443655b401d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"fluid.small-scale.anomalous-exponents","kind":"phenomenon","literature_status":"open","n":"1","parents":[],"plain":"In turbulence, velocity differences between two points grow with their separation, and the simplest theory (Kolmogorov 1941) predicts how; measurements show rare violent events that break this prediction more and more strongly for higher statistical moments. Nobody can yet calculate the observed deviations from the equations of fluid motion.","posed_since":"1962","precise":"System: statistically stationary, homogeneous, isotropic turbulence of the 3D incompressible Navier-Stokes equations at $\\mathrm{Re}_{\\lambda} \\to \\infty$. Quantity: inertial-range exponents $\\zeta_{p}$ in S_p(r) = <|delta_r u|^p> ~ r^zeta_p, which deviate from the Kolmogorov 1941 value $p/3$ (measured $\\zeta_{6} \\sim 1.78$, approximately). Answer: a derivation of zeta_p from the Navier-Stokes equations, or from an approximation with controlled error, that reproduces measured values for p up to about 10 and identifies the flow structures responsible.","problem_ref":null,"references":"","settled_by":"A first-principles calculation of $\\zeta_{p}$ that matches high-resolution DNS and experiment within error bars for $p\\ \\text{up to}\\ 10$.","status_note":"Multifractal and log-Poisson models fit the data with adjustable inputs; no first-principles derivation exists as of 2026.","title":"Origin of anomalous scaling exponents in three-dimensional turbulence","topic_ref":"45474d2178078204b5f1dbc4ca64d4b74ada936d74d13eddb4d83cc4b1e3c985"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"70b03dbd933ef88fa9a98dc1f0036ecb69609888555d805ef03d9f8956caae39","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"e1cf18486669ed8cbbbb03e228a0a7825ebaed5aa6175afde5e76fcfce0585b3","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"3sk_Escm75wm4wziOiz-R51XOBp5vnVOkZUwME751rowk9VhiORyA216q1z_qeBDJU4FKSaRNg5nVAtC8nrUDA"},"schema":"pubphys.envelope/1"},"record_hash":"70b03dbd933ef88fa9a98dc1f0036ecb69609888555d805ef03d9f8956caae39","leaf_index":1433}