Are results of a turbulent flow experiment repeatable? Say I perform a simple pipe flow experiment. I make sure that the Reynolds No. is sufficiently high so that the flow is turbulent. I measure the velocity field using probes placed at different points of the tube. Now, I perform the same experiment 24 hrs later at the same initial and external conditions as the previous run. Theoretically, will I get the exact same velocity profile as the previous run?
I know that the system of equations governing the flow is chaotic i.e a very very slight change in the initial conditions will lead to a different result. For laminar flow, it's possible to replicate the results. I want to know that if the conditions are kept identical, can we replicate the results of turbulent flow.
 A: It depends on what you mean by "same."
If you mean the exact same values at each instant in time at each position in space, then no -- it is not repeatable. As you mentioned, the system behaves chaotically and there is no way to ensure the initial conditions are the same. You can't control where every single molecule of the gas is and what direction it is headed at the initial conditions, even with perfect equipment. In reality, you'll find that even the best experiments don't hold boundary conditions exactly the same, even within the same run, let alone between days.
But there are other meanings of "same" that would be repeatable. The time-averaged velocity profiles, for example, should be highly repeatable if your experiment is carefully configured. Likewise, low-order moments are probably also quite repeatable. Ultimately any form of statistical information should be repeatable, given enough samples over which the statistics are computed. Depending on the type of the probe, it may be performing a sort of averaging for you (i.e. the probe samples a non-negligibly-small volume from which it reports its values), and so you may see some repeatability due to that averaging over the sampling volume.
This is why, almost always, experiments (and simulations) of turbulent flows report statistical quantities and almost never report instantaneous, point values -- except to show what the underlying data may look like. It's also why I really stress to the people I work with that no results we ever really show are the "same"; at best, they are "similar" because we will never get two datasets that are exactly identical.
A: Yes, it is repeatable. This doesn't just go for the results of a turbulent flow experiment, but generally for any experiment involving chaos as an active component.
Chaos/turbulence determines a margin of freedom in the result, so the experiment the next day will give you a result within the exact same margin. More experiments allow you to narrow down the margin to a minimum, but it will not disappear until you can fully control the turbulence, at which point it stops being turbulence.
A: As you rightly mentioned Turbulent flow is chaotic.
From Theoretical point of view, YES you can in principle, you can exactly replicate the system provided you give the initial condition exactly same as before to infinite precision. After all chaotic systems are deterministic system.
From practical point of view, NO you cant, the reason is very straight forward. Any physical measuring instrument has a precision limit. It can never be infinity precise. Hence even if you replicate the system with a 10 decimal places precise initial condition, there is still an error in the higher decimal places, although its negligible initially, chaotic system implies these errors add up over time and doesn't average to zero like it would do  in non-chaotic system, hence in some time the replicate system will start to deviate significantly as soon as the errors are large enough.
To study such systems we use statistical methods and averages instead of pinpointing each molecular level motion, now although velocity of each individual molecules can't be exactly replicated, the average values can still be replicated.
