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Whether this hard limit exists in real turbulence, and what sets its value, is still studied.","posed_since":"1969","precise":"For flows with energy spectrum E(k) ~ k^(-beta) over an inertial range, Lorenz predicted that for $\\beta < 3$ the predictability time $T_p$ stays bounded as the initial error amplitude $\\delta_0 \\to 0$ at fixed error scale, since error moves upscale in eddy turnover times $\\tau(k) \\sim k^{((\\beta-3)/2)}$. Determine whether this holds for 3D Navier-Stokes turbulence ($\\beta = 5/3$) as the Reynolds number grows, and how $T_p$, in units of the large-eddy turnover time, depends on the dissipation range and on the scale of the initial error. Answer: yes or no, with T_p and its dependences.","problem_ref":null,"references":"","settled_by":"Identical-twin direct numerical simulations over many decades of $\\delta_0$ and a range of Reynolds numbers, showing saturation of $T_p$ and its value.","status_note":"Identical-twin simulations of 3D turbulence and of atmospheric models support a finite horizon; its dependence on the dissipation range is debated.","title":"Finite predictability horizon in multiscale chaotic 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