{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d75133d9a253e6bddc98a1545f0e042804e86ec4d77831ed0407bf1db166c3bb","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3fbd69cf67f68ee9dfc5842314a7b44c43a610306ecf77aeffc287160438a2bf","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.small-scale.zeroth-law","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Experiments suggest that turbulent energy loss stays finite even as the fluid viscosity is made vanishingly small, a property called the dissipation anomaly. Recent large simulations without walls hint that the effect may instead fade very slowly as the flow speed grows.","posed_since":"","precise":"Let $D = \\epsilon L / U^{3}$ be the mean kinetic-energy dissipation rate $\\epsilon$ normalized by rms velocity $U$ and box scale $L$, for body-forced Navier-Stokes turbulence in a periodic box. As $\\mathrm{Re} = U L / \\nu \\to \\infty$, does $D$ tend to a positive constant (strong anomaly), or decay as $\\mathrm{Re}^{-\\alpha}$ with small $\\alpha > 0$ (weak anomaly)? A strong anomaly requires $\\zeta_3 \\le 1$ for absolute increments; $\\zeta_3 > 1$ forces $D \\to 0$ and bounds alpha from below. Answer: the limit of $D$, or $\\alpha$ with error bar, shown to be independent of forcing details.","problem_ref":null,"references":"","settled_by":"DNS of periodic-box turbulence over at least one further decade of Re, or a laboratory flow without walls, resolving whether D(Re) levels off or keeps decreasing.","status_note":"2025 periodic-box DNS (Iyer, Drivas, Eyink, Sreenivasan, arXiv:2504.13298) report $\\alpha \\sim 0.05$ and $\\zeta_{3} \\sim 1.07 \\pm 0.07$, consistent with a weak anomaly; flows with walls or bluff bodies show $D \\to \\mathrm{constant}$.","title":"Is the dissipation anomaly strong or weak in wall-free 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