As ekelsen mentioned, you probably were not doing a direct numerical simulation (DNS; using NS specifically) and instead were using an approximation to NS which

As ekelsen mentioned, you probably were not doing a direct numerical simulation (DNS; using NS specifically) and instead were using an approximation to NS which has much lower computational cost/complexity but also reduced accuracy. Good LES would converge to the DNS result if the grid were fine enough. The term for this sort of error is "model inadequacy error", that is, error from the model being wrong. My impression is that so far DNS matches experimental results well given that the experiment actually represents the situation of interest. For example, I am aware that at least some "Kelvin-Helmholtz" experiments don't match DNS well at all, and the DNS is considered more credible than the experiments because in the DNS case you know all of the inputs, whereas in the experiments the initial conditions might be close to the desired case, but apparently not close enough. (The Kelvin-Helmholtz instability is of fundamental importance but is not easy to obtain in isolation experimentally.) "Sensitivity dependence on initial conditions"/chaos means that close may not be enough. There also is the issue of numerical error from the fact that you are using discrete equations, but usually simulators take steps to check this is negligible. (Which may not be enough.)