{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"53e58e9107f0665d4f5920fb828229f6ff6eb4908d36d9328ccfd5ceeb304606","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"8ce48874d473900d3c82eb6818a8aa15267e56d69fdcc3ea9ec5c9ab522689b0","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.wall-turbulence.drag-reduction-scaling","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Moving a wall sideways back and forth, or in travelling waves, can cut turbulent friction by tens of percent. Whether a net energy saving survives at the very high speeds of ships and airliners is unknown.","posed_since":"","precise":"For channel or boundary-layer flow with spanwise wall velocity $W(x,t) = A \\sin(k_x x - \\omega t)$, determine the maximum net power saving $S$ (drag reduction minus actuation power, as a fraction of uncontrolled pumping power) over $(A, k_x, \\omega)$ as a function of $\\mathrm{Re}_{\\tau}$, and its limit as $\\mathrm{Re}_{\\tau} \\to \\infty$. At $\\mathrm{Re}_{\\tau} \\sim 10^3$ drag reduction reaches about 30 percent; experiments at $\\mathrm{Re}_{\\tau}$ of order $10^4$ report net savings with actuation tuned to large scales.","problem_ref":null,"references":"","settled_by":"Experiments or wall-resolved simulations at $\\mathrm{Re}_{\\tau}$ from $10^4$ to $10^5$ with measured actuation power, giving $S(\\mathrm{Re}_{\\tau})$ over that range.","status_note":"Predictions of a slow decline of drag reduction with Re (Gatti and Quadrio 2016) and 2021 high-Re experiments with large-scale actuation (Marusic et al.) leave the asymptotic trend open.","title":"Does spanwise wall forcing still save net power at very high Reynolds 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