{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"c53ff0095b197f8c57c31a5162a02b21a85350d2e1cbab3ddb3cb0cb535ac2d6","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"411084c67c5239051b97b19d368c9a4e16b3fb74d90f83735f90fe7e308160e8","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"fluid.wall-turbulence.near-wall-peak","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"The strength of turbulent fluctuations just above a wall, measured relative to the wall friction, keeps rising as the flow gets faster in all experiments so far. Whether it rises forever or levels off is disputed, and the data cannot yet decide.","posed_since":"","precise":"The inner peak of the streamwise variance $\\langle u'^2\\rangle+$ at $y+ \\sim 15$ grows roughly as $3.7 + 0.64\\operatorname{ln} \\mathrm{Re}_{\\tau}$ (approximately) in channel DNS for $\\mathrm{Re}_{\\tau}$ from 180 to about $10^4$. As $\\mathrm{Re}_{\\tau} \\to \\infty$, does it diverge logarithmically (attached-eddy prediction) or approach a finite limit with corrections of order $1/\\operatorname{ln} \\mathrm{Re}_{\\tau}$ or $\\mathrm{Re}_{\\tau}^{-1/4}$? Answer: the asymptotic form, with evidence beyond $\\mathrm{Re}_{\\tau} \\sim 10^5$ where the competing fits separate.","problem_ref":null,"references":"","settled_by":"Well-resolved near-wall measurements or DNS at $\\mathrm{Re}_{\\tau} \\sim 10^{5}$ or above distinguishing logarithmic growth from saturation.","status_note":"Chen and Sreenivasan (2021), Monkewitz (2022) and Hwang (2024) argue for a bound; Jimenez (2024, arXiv:2408.09259) argues the peak probably grows in wall units while vanishing relative to the bulk velocity.","title":"Does the near-wall peak of streamwise fluctuations grow without 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