https://www.quantamagazine.org/mathematicians-prove-batchelors-law-of-turbulence-20200204/

Picture a kitchen sink full of water. Open the drain. The water in
the sink will start to rotate nearly as a single body. If you zoomed in on the
fluid and measured its velocity at finer scales, you’d still observe the same
thing — each microscopic portion of the fluid moves in lockstep with the others.

“The motion is predominantly at the scale of the sink itself,” said Blumenthal,
a postdoctoral fellow also at the University of Maryland, College Park.

Now imagine that instead of merely draining the water, you pulled the plug while
also adding water jets to the sink, churning it like a jacuzzi. With the naked
eye, you might observe a handful of different vortices rotating in the water.
Choose one of the vortices and zoom in on it. If you were a mathematician trying
to analyze the flow of the turbulent sink, you might hope that every particle of
water within that chosen vortex was moving in the same direction. This would
make the task of modeling the fluid easier.

But alas, you’d find instead that the vortex is itself made up of many different
vortices, each moving its own way. Zoom in on one of those and you’ll see that
it, too, is made up of many different vortices, and so on all the way down,
until the effects of internal friction (or viscosity) within the fluid take over
and the flow smooths out.

This is a hallmark of turbulent systems — they feature distinct behaviors nested
within each other at different scales. In order to fully describe the motion of
a turbulent system, you need a picture of what’s going on at all of these scales
at each moment in time. You can’t ignore any of them.