{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d44d6ac8ede4443e688a0848ebaa498e702f9f683fb7579f54451c7104347af3","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","d3e6dd0e0a8cfc36ca8135ffa5a96e2bf6c255854d386a540399d70424adbe1f"],"salt":"7c3d885e4522b70f1ff6c906158f17a2ed0fa3105acb0f4688ada3ddcea1a1d2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"fluid.small-scale.scalar-skewness","kind":"well-posed","literature_status":"open","n":"2","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":"d3e6dd0e0a8cfc36ca8135ffa5a96e2bf6c255854d386a540399d70424adbe1f","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 $\\mathrm{Sc} \\sim 1$ the derivative skewness stays of order 1 up to the highest $\\mathrm{Re}_{\\lambda}$ measured; DNS at $\\mathrm{Re}_{\\lambda} 140 \\text{ to } 650$ show isotropy is restored as Sc grows at fixed $\\mathrm{Re}_{\\lambda}$ (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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"846db98d72b9f35bf6ae140a5eabd3d19b8d8d771b878351528d3b0b307d0451","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"4b273e2b18649467873ae35e705f23183a29951beb1d47837b60adf8fcc61988","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"15WjS6slZJFyzm7RWEGoQQwJsmFXLOEKTTJG8uUJ4O61XCJBlIBjFIn3F-09gXa3YkeUwvumUhEyRYwfl3x_CA"},"schema":"pubphys.envelope/1"},"record_hash":"846db98d72b9f35bf6ae140a5eabd3d19b8d8d771b878351528d3b0b307d0451","leaf_index":3280}