{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d1e40cbd20ef90323e0efd72b41015921971ab704607296c362e8abf2c0e41c5","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"91226c0ee316773732531cb437b55858497e72af34c88728630155ddd0e6db22","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.2d-turbulence.enstrophy-log-correction","kind":"well-posed","literature_status":"open","n":"1","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":null,"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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