{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"278888c2f16d00e2d66a7728d85de09e3ea88a7957e8f12faaa503503e6f5f1a","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","e56dee8e483b63170b176f42eece5008c26ad2f4d4c73249e8fde9ac6bd575aa"],"salt":"e494ec005246553e79f960e59f1f7334947d44f96851fe01ed6355172ff178ba","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"fluid.2d-turbulence.enstrophy-log-correction","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Flat turbulence also sends enstrophy (the mean squared spin of the fluid) to small scales, and theory predicts the energy spectrum there with a small logarithmic correction. That correction has not been confirmed.","posed_since":"1971","precise":"In the direct enstrophy cascade of forced 2D turbulence, Kraichnan (1971) predicted $E(k) = C' \\eta^{2/3} k^{-3} [\\ln(k/k_f)]^{-1/3}$, with $\\eta$ the enstrophy flux and $k_f$ the forcing wavenumber. In the limit of vanishing large-scale friction and $k/k_f \\to \\infty$, verify or refute the exponent $-1/3$ of the logarithm and determine $C'$.","problem_ref":"e56dee8e483b63170b176f42eece5008c26ad2f4d4c73249e8fde9ac6bd575aa","references":"","settled_by":"DNS with negligible large-scale friction over about three decades of $k/k_{f}$, fitting the logarithmic factor with error bars.","status_note":"Linear friction steepens the spectrum and masks the correction (arXiv:2511.08220, 2025).","title":"Logarithmic correction in the two-dimensional direct enstrophy 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