Real-World Turbulence as Dissipative Euler Solutions: A Physics Perspective Gregory Eyink Johns Hopkins University Since Onsager’s proposal in 1949 that turbulent velocity fields at high Reynolds number may be considered as dissipative weak solutions of the Euler equations, there has been extensive work in the mathematics community, but almost no exploitation of the theory by physicists. This seems to be due to the fact that its physical meaning remains obscure to most fluids scientists. However, as we show here, Onsager’s theory can be understood most intuitively as an application of the concept of “renormalization-group invariance” to the problem of explaining the available experimental data on anomalous energy dissipation. Such anomalies imply diverging velocity gradients in the inviscid limit, or a ``violet catastrophe’’ in Onsager’s own words. Regularizing this ultraviolet divergence, e.g. by a spatial coarse-graining at length-scale ??, leads to a description of turbulent velocities as “coarse-grained Euler solutions” at scales ?? in the inertial range. As we show, this notion of “coarse-grained solution’' is equivalent to the mathematical concept of “weak solution” when the length-scale ?? can be taken arbitrarily small; it also underlies the practical turbulence modeling method of Large-Eddy Simulation. Since spatial coarse-graining is a purely passive operation (“removing one’s spectacles”), no physics can depend upon the arbitrary scale ??. A consequence of this arbitrariness is Onsager’s experimentally confirmed prediction of (near) singularities with Hölder exponent h