Averaging in turbulent flow

i have simulated Turbulent flow around a wall-mounted cube with LBE-LES. but my question is not about LBE, its about turbulent, when i want to validate my results:all papers compare mean-quantities. my question is here how i calculate mean-quantities from instantanous-quantities.
i did this way: for example i sum ux in one points of domain in 40000 time step and then divided the answer by 40000. am i true?
let me say in in the other way.we know that turbulent isunsteady, so how can we show a streamline and say it is the streamlines of this flow(in fact beacuase of being unsteady the streamlines should change every time). Please help me.


If you are running a LES, the simulated quantities correspond already to space-averaged values. But you are looking for even more averaging, right? If I understand you right, your simulation is statistically stationary, while the actual LES is time-dependent. I think that a common approach to obtain the stationary mean values is to compute a time average. Such an approach is based on an assumption of ergodicity, which claims that the time average converges to the same value as an ensemble average over equivalent realizations of the flow. The problem with time averages is that it is difficult to know when they have converged. To put it the other way round, it is difficult to know over which time window you should average your values. Turbulent flows often possess rare events which do not occur within a chosen time frame. In these cases, it looks like your time average has converged, while in reality it might further change if you extend the time window to include a few samples of the rare events.