{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3c47090792905a929e1e51f6e705b57955c16453d276a2ab52089fe0397f742b","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"343531416051814c4a1a9c39823d2976c8a3b64ae7434d51618806330592ac78","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.small-scale.kolmogorov-constant","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The energy spectrum of turbulence has a known shape with one dimensionless prefactor, the Kolmogorov constant, measured near 1.6. No calculation from the equations of motion produces this number with an error that the method itself controls.","posed_since":"","precise":"In the inertial range $E(k) = C_K \\epsilon^{2/3} k^{-5/3}$ up to small intermittency corrections, with measured $C_K \\sim 1.5 \\text{ to } 1.7$ (approximately). Compute $C_K$ from the Navier-Stokes equations by a closure (Lagrangian closures of Kraichnan type, eddy-damped quasi-normal Markovian closure, functional renormalization group) in which the neglected terms are bounded or shown to be small. Answer: a value with an error estimate derived within the method.","problem_ref":null,"references":"","settled_by":"A closure or renormalization-group calculation with a demonstrated small parameter or convergent truncation giving $C_K$ within the experimental range.","status_note":"Existing closures and renormalization-group calculations give values near the measured range but rely on uncontrolled truncations or expansion parameters set to physical values.","title":"Controlled closure calculation of the Kolmogorov 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