[btrettel]

It seems popular to believe that for fluids in general forecast accuracy is dominated by errors in the initial conditions (ICs), but my own look at the problem suggests that's not so clear. I recall skimming a book on forecasting by a weather forecaster and he addressed this misconception. It appears that there are multiple sources of error, from errors in the ICs to numerical integration to the fact that the models they use are approximate (i.e., they don't solve NS; they solve a filtered version of NS with a turbulence model and additional models for other physics like chemistry), etc. My impression is that the dominant two are model inadequacy (the models are approximate) and compounded errors due to IC errors and non-linearity, but which is larger likely depends on the problem, and I am not particularly confident about this in general as I don't have hard data. (Certain types of turbulence models get more accurate as the resolution/computational cost increases, but I can't speak for other models. This fits with what you said about lack of computational power.)

The right way to do this is through uncertainty quantification techniques, and I don't know a lot about those at the moment. Until then, all I can say is that there are multiple sources of error.