What happens with turbulence and chaotic systems in general is that if your initial conditions change a little bit, then your final result becomes random. One way of thinking about this is imagine a particle near a turbulent field. If you change the initial conditions slightly, that particle could end up *anywhere*. If you care where all of the particles end up, you are stuffed, because where an individual particle ends up is random.But surely this means all solutions that are true for initial condition changes are over simplified and provide an approximate solution in reality?
What this says is that the "reductionist" approach wouldn't work, you have to try something else.
You usually don't care about tracking every particle. What you care about are "generalized quantities" (i.e. if I put this shape in this gas, what's the drag coefficient). There are a number of techniques for figuring that out.
It's not that fluids are particular complex, it's just undergraduate physics classes are deliberately oversimplified. The types of systems that you learn about in undergraduate physics are *deliberately* selected not to show complex behavior, and this is in part because engineers *deliberately* build systems that minimize weird behavior. So what happens is that physics undergraduates learn a "cookbook" of tools that work for certain rather simple systems. The mistake is thinking that you can use the cookbook for everything.Is it that fluids are so complex that this over-simplification is more pronounced when initial conditions are altered?