Turbulence and Repeatability

It's well known that in fluid flow that becomes turbulent, details of the turbulent motion are quite unpredictable. Set up an experiment as identically as possible and watch the detailed motions over and over, and they will vary dramatically. Motions of individual tracers, velocities at a given point in space and time vary drastically for experiment to experiment - and moment to moment. Statistically, though, the behavior is quite consistent. Average over a large number of runs of the experiment, and the average of velocities and distribution of trajectories becomes quite consistent.

These facts underly the well-know inability of scientists to accurately predict the weather a few days from now, and their much better capability to predict the average long term weather - aka the climate.

These properties apply not only to actual physical experiments, but also to numerical experiments modelled on the physical experiments.

The story for long-term climate prediction is considerably more complicated, but this theme is an important aspect. More on the complications later.

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