{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"64fcdf0bccae48c3fe28060babda52bef9eba59f79cd7ccf7a22b4b3fbebf79e","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"54dbc30f163430df1bb25b6e42696b65b5d67466db7dfbc6c6478a4b81616764","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"fluid.2d-turbulence.conformal-invariance","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In flat turbulence, the curves where the local spin of the fluid changes sign look statistically identical to the boundaries of random clusters in a classic model of percolation, a symmetry known from equilibrium critical points. Why a driven, dissipative flow should have this symmetry is unexplained.","posed_since":"2006","precise":"Forced 2D incompressible Navier-Stokes turbulence with large-scale friction, inverse-cascade range $\\ell_f \\ll r \\ll L$. Zero-vorticity isolines are statistically consistent with Schramm-Loewner evolution $\\mathrm{SLE}_{\\kappa}$ with $\\kappa = 6$ (Bernard, Boffetta, Celani, Falkovich 2006), the class of critical percolation cluster boundaries. Is this conformal invariance exact as $L/\\ell_f \\to \\infty$, and which property of the dynamics implies it? Answer: a derivation, or a measured deviation of $\\kappa$ beyond error bars.","problem_ref":null,"references":"","settled_by":"An analytic derivation from the $2\\mathrm{D}$ Navier-Stokes dynamics, or a high-precision numerical test of $\\kappa$ and of the conformal covariance of multipoint observables.","status_note":"Evidence is numerical and experimental; a 2025 theoretical proposal models the cascade as constant-flux domains whose boundaries carry a Liouville conformal field theory (Eling, arXiv:2505.09657), without derivation from the Navier-Stokes equations.","title":"Are inverse-cascade vorticity isolines exactly conformally invariant?","topic_ref":"0182f1f595a8d4484a77534cfdcf00e164a201f0557ef3e8a7e29298531a113e"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"29658abd245488d7bdaca98de2977ecfc73df9c00ca4631faa8f7b546453dd06","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7ee65291ed9d62722e238046c3f4ced9e109ce4532676aa4e2235b155c32ff3a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Hknc7HmiWrPBtXtTC57mMvA3oWobWTNSFGz8TiZz3QZ9Bz22QY-W6YCJTb4ub2MEnKnHJwr-botpN8Z5VLMjCw"},"schema":"pubphys.envelope/1"},"record_hash":"29658abd245488d7bdaca98de2977ecfc73df9c00ca4631faa8f7b546453dd06","leaf_index":1389}