Suppose you want to solve the Navier-Stokes equation for an incompressible turbulent flow. This is, in principle, possible. However, for higher Reynolds number, this isn't really feasible since the smallest eddy sizes are really small. First question 1) Why would this prevent you from computing a solution? I can't actually imagine in my head the computation procedure, and why having tiny eddies is different from just having small eddies? Surely you have to compute the whole flow field anyway? Second & Third questions Turbulent flows have two important characteristics: > acute sensitivity to initial conditions, meaning a precise deterministic prediction of the flow is impossible. > velocity has a reproducible (and hence, predictable?) mean component, and a chaotic, fluctuating component. 2) Doesn't the first statement mean that DNS is useless anyway? If you can't specify initial (and boundary and material) conditions for the mathematical model (the Navier-Stokes equations) to be exactly the same as the real life, then your calculated solution will be wrong? 3) Is the fact that the mean is reproducible (predictable) the basis of the RANS models? Like, we can predict the mean component, and we make some assumptions (like eddy-viscosity hypothesis) about the fluctuating? I would have written three separate questions, but they are all related – how to predict the velocity field in a turbulent flow field?