{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"87dbd5fcee0140f57f1878c54897df4135eb95ce2c7d7f3d166dd5ba421009f2","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"115306444281ecb400545837a7c07c8708d3e9f30b0ec6400de066cc0e7e4cdf","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.wall-turbulence.karman-constant","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Close to a smooth wall, the mean speed of a turbulent flow grows with the logarithm of distance from the wall, with a slope set by the von Karman constant. Pipes, channels and boundary layers give slightly different values, and it is unclear whether one number holds for all.","posed_since":"1930","precise":"In the overlap layer of smooth-wall turbulence, $U+ = (1/\\kappa) \\ln y+ + B$, with $U+ = U/u_{\\tau}, y+ = y u_{\\tau}/\\nu$ and $u_{\\tau}$ the friction velocity. Determine the $\\mathrm{Re}_{\\tau} \\to \\infty$ limit of $\\kappa$ for pipe, channel and zero-pressure-gradient boundary layer, and whether the three coincide; reported values range from about 0.37 to 0.42. Answer: $\\kappa$ for each flow with uncertainty below 0.005.","problem_ref":null,"references":"","settled_by":"High-accuracy wall-shear and profile measurements in all three geometries at $\\mathrm{Re}_{\\tau} > 10^{4}$ with matched instrumentation, plus DNS at $\\mathrm{Re}_{\\tau} \\sim 10^{4}$ or above.","status_note":"Flow-dependent values were proposed by Nagib and Chauhan (2008); pipe facility data and channel DNS up to $\\mathrm{Re}_{\\tau} \\sim 10^{4}$ have not closed the question.","title":"Is the von Karman constant universal across wall-bounded 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