This happens for exactly the same reason as in a real fluid, or, for that matter, in various examples that we saw in Chapter 7: even though at an underlying level the system consists of discrete particles, the effective randomness of the detailed microscopic motions of these particles makes their large-scale average behavior seem smooth and continuous.

We know from physical experiments that the characteristics of fluid flow are almost exactly the same for air, water, and all other ordinary fluids. Yet at an underlying level these different fluids consist of very different kinds of molecules, with very different properties. But somehow the details of such microscopic structure gets washed out if one looks at large-scale fluid-like behavior.

Many times in this book we have seen examples where different systems can yield very much the same overall behavior, even though the details of their underlying rules are quite different. But in the particular case of systems like fluids, it turns out that one can show—as I will discuss in the next chapter—that so long as certain physical quantities such as particle number and momentum are conserved, then whenever there is sufficient microscopic randomness, it is almost inevitable that the same overall fluid behavior will be obtained.

So what this means is that to reproduce the observed properties of physical fluids one should not need to make a model that involves realistic molecules: even the highly idealized particles on the facing page should give rise to essentially the same overall fluid behavior.

And indeed in pictures (c) and (d) one can already see the formation of a pair of eddies, just as in one of the pictures on page 377.

So what happens if one increases the speed of the flow? Does one see the same kinds of phenomena as on page 377? The pictures on the next page suggest that indeed one does. Below a certain critical speed, a completely regular array of eddies is formed. But at the speed used in the pictures on the next page, the array of eddies has begun to show random irregularities just like those associated with turbulence in real fluids.

So where does this randomness come from?

In the past couple of decades it has come to be widely believed that randomness in turbulent fluids must somehow be associated with

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From Stephen Wolfram: A New Kind of Science [citation]