{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"f29f0c19b9636b114852b01d52af288f5a132808d02bbab9f5bd01e05c218fa6","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a96f7e2e8f03c3e9c5b08d0df09c4e1b1a620162980853e7db29c6fb58db21ee","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"fluid.small-scale.scalar-skewness","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"When turbulence stirs a dye or temperature that varies steadily in one direction, the small-scale ripples of the dye keep a preferred direction even at the highest speeds tested. This contradicts the textbook expectation that small scales forget large-scale directions, and whether the memory ever disappears is unknown.","posed_since":"","precise":"For a passive scalar $\\theta$ with uniform mean gradient $G$ in turbulence, the skewness $S = \\langle(\\mathrm{d}\\theta/\\mathrm{d}x)^3\\rangle/\\langle(\\mathrm{d}\\theta/\\mathrm{d}x)^2\\rangle^{3/2}$ of the scalar derivative along $G$ is of order 1 in experiments and DNS for $\\mathrm{Re}_{\\lambda}$ from about $10^2$ to $10^4$, whereas local isotropy requires $S \\to 0$. Does $S \\to 0$ as $\\mathrm{Re}_{\\lambda} \\to \\infty$ at Schmidt number $\\mathrm{Sc} \\sim 1$, and at what rate? Answer: the limit of $S$ and its $\\mathrm{Re}_{\\lambda}$ dependence.","problem_ref":null,"references":"","settled_by":"Measurements or DNS of $S$ over $\\mathrm{Re}_{\\lambda}$ from $10^3$ to $10^5$ at $\\mathrm{Sc}\\sim 1$ showing a definite trend.","status_note":"At $Sc \\sim 1$ the derivative skewness stays of order 1 up to the highest $Re_{\\lambda}$ measured; DNS at $Re_{\\lambda} 140 \\text{ to } 650$ show isotropy is restored as Sc grows at fixed $Re_{\\lambda}$ (Buaria, Clay, Sreenivasan, Yeung, PRL 2021), a ramp-cliff model fitting the trend.","title":"Does small-scale anisotropy of a mixed scalar vanish at high Reynolds number?","topic_ref":"45474d2178078204b5f1dbc4ca64d4b74ada936d74d13eddb4d83cc4b1e3c985"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d3e6dd0e0a8cfc36ca8135ffa5a96e2bf6c255854d386a540399d70424adbe1f","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"1f0ebeaa1d3afa74d4868520c0e8e44cc63cd92ed20607f7346ec04bac511c21","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"fs7dL2inVJfapBZZmfGsZ5CjX7WuKOYppgRw0yCvnD6z8ci8kVEao1XXflLWUFG88D5IMPae81cWPtzUGXsmBw"},"schema":"pubphys.envelope/1"},"record_hash":"d3e6dd0e0a8cfc36ca8135ffa5a96e2bf6c255854d386a540399d70424adbe1f","leaf_index":1438}