
Because fluid dynamics is so hard,

many people try to come up with toy models to at least get a glimpse

of what's happening.

One of these toy modelsa particularly interesting oneis the Lorenz system.

By the way, this name is not to be confused with that of the physicist who spelled with "tz."

This is what is described by this model.

There is a layer of incompressible liquid between a surface of constant high temperature

and a surface of constant low temperature.

We've got some melting icecubes here.

The velocity field in that liquid is described by three highly abstract parameters,

called x, y, and z.

They describe the relative amount of different sorts of motion.

Even though this is a very sketchy and abstract description,

some people have succeeded in implementing these equations

with an actual water wheel.

The idea about studying these equations is that they may be telling us something

about every system in which convection is present.

When we plot the solutions of the Lorenz system in 3D this is what we get

a very intricate butterflylike pattern.

Here we're seeing two solutionsone in green and one in blue

starting from almost the same pointsomething to explore in the next section.

The trajectories make some turns on one ring, then jump to the other ring,

jump back to the first ring and so on.

The number of turns they take per ring seems to be almost unpredictable.

There is one more thing.

Even though both trajectories have almost the same starting point,

you can see that they quickly diverge in the course of time.

We're going to study that in the next segment.