{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"40be350ef5d9ad7fb490f7ab07f246d39effcaf5fe1c814c2b9c8432f125f462","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"6a6a7157495f2ca2a17a4b4108685d446cf0d000636ade5b09d717ca9a6857f0","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"fluid.small-scale.lagrangian-bridge","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"The velocity of a single fluid particle followed in time shows rare violent jumps, just as velocity differences between two points in space do. Whether the jumps along a particle path are fully predictable from the spatial ones, at all flow speeds and statistical orders, is not established.","posed_since":"","precise":"For homogeneous isotropic turbulence, Lagrangian structure functions $S_{p}^{L}(\\tau)=\\langle\\mid v(t+\\tau)-v(t)\\mid^p\\rangle\\sim \\tau^{\\zeta_{p}^{L}}$ for $\\tau_{\\eta} << \\tau << T_{L}$ (Kolmogorov time to Lagrangian integral time). The multifractal bridge, which maps the Eulerian singularity spectrum $D(h)$ to Lagrangian statistics through $\\tau\\sim r/\\delta_{r} u$, predicts $\\zeta_{p}^{L}$ from the Eulerian $\\zeta_p$. Determine whether this prediction holds as $\\mathrm{Re}_{\\lambda}\\to \\infty$ for p up to about 8, including the contribution of particles trapped in vortex filaments at small $\\tau$. Answer: $\\zeta_{p}^{L}$ with error bars compared with the bridge prediction.","problem_ref":null,"references":"","settled_by":"Lagrangian particle tracking in experiments and DNS above $\\mathrm{Re}_{\\lambda} \\sim 2000$ with converged high-order moments over at least a decade of time lags, compared with Eulerian exponents from the same flows.","status_note":"Eight experimental and numerical data sets at $\\mathrm{Re}_{\\lambda}\\ 120\\ \\text{to}\\ 740$ collapse and are captured by a multifractal description (Arneodo et al., PRL 2008); convergence at higher $\\mathrm{Re}_{\\lambda}$ and higher orders is not established.","title":"Do Lagrangian intermittency exponents follow from Eulerian ones?","topic_ref":"45474d2178078204b5f1dbc4ca64d4b74ada936d74d13eddb4d83cc4b1e3c985"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b94c0384664839938a9c632e5cf40672f0c81e8e48f2f3d37290c7f7cec076e6","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"76c4946719333d52b60cfd454fc030584e44b77e1fc631066784f9c07196fd35","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"W35O84mkpzsgfqOoTw5WZy97YUY8prRlmjNwNeQQZByuWMBIsK5QP5dF-_JDpMo9KNYJVOgf1BzpcY3OaBsRCg"},"schema":"pubphys.envelope/1"},"record_hash":"b94c0384664839938a9c632e5cf40672f0c81e8e48f2f3d37290c7f7cec076e6","leaf_index":1437}