{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"efa7d7904167dc75a3e68ff02c194bff82b446ead09ebf55e024e850fc6203eb","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4ae796e9db59211c03f77d6c05df7ec4dd53ba603e78c8e02c4a1e4e0cc574a9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.elastic-turbulence.spectrum-exponent","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The chaotic flow of polymer solutions has an energy spectrum that falls off steeply toward small eddies. Whether its slope is the same in all flows is unknown.","posed_since":"2003","precise":"In elastic turbulence at $\\mathrm{Re} \\to 0$ the velocity spectrum is $E(k) \\sim k^{-\\alpha}$; theory requires $\\alpha > 3$ for a smooth velocity field (Fouxon and Lebedev 2003), experiments in curvilinear flows report $\\alpha$ of about 3.3 to 3.6 (approximately), and channel DNS give $\\alpha \\sim 4$. Determine whether $\\alpha$ has a universal value as $\\mathrm{Wi} \\to \\infty$ and, if so, compute it.","problem_ref":null,"references":"","settled_by":"A theory predicting $\\alpha$, confirmed by spectra over at least a decade in $k$ in two different geometries at matched Wi.","status_note":"2024 channel simulations report $k^{-4}$.","title":"Is the velocity spectrum of elastic turbulence universal?","topic_ref":"b3c75da8fa5e430744454ba9d543f14e3e260933f89d866cf5e627ef69411678"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3d5c7e2dc3a7c2c18bcea67916c5241fa9c0a2a509e1b74c657f1095fb1f2a0e","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"52d7f824eaa434407c9892796d83e11cb57042b3584b052bb7550c6e8f52049b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"P7h8XDwDs18Qf0qMkCC7uHIB3GoDolNJAjKN16QUonz9LxRVxMK5IE9dAPiB-raPZ9DphipRDR8-jYJGhiH5DQ"},"schema":"pubphys.envelope/1"},"record_hash":"3d5c7e2dc3a7c2c18bcea67916c5241fa9c0a2a509e1b74c657f1095fb1f2a0e","leaf_index":1412}