Meander

If we have some kind of slope and deposit a drop of water on it, the water will run directly down the slope. It won't go up for a bit before turning down. It won't run across the slope a ways. It will go as straight down as possible. So why is it that rivers, which are just water running down a slope, meander?

When I was a kid I learned an explanation that was neat, plausible, and wrong: That the ground isn't perfectly smooth, so as soon as the flow bends around an obstacle you have a curve where water is flowing slowly on the inside and fast on the outside. Then the outside erodes more than the inside (which is actually depositing material instead of eroding because of water slowing down) and the curve gets bigger and the process continues getting more extreme until you get big meanders.

There is a major problem with that explanation, in that water does not flow more quickly at the outside of a bend, it flows more slowly. This is vortex flow. Think of a whirlpool in a bathtub. That water is flowing in a curve around the drain with the water on the inside edge right at the drain going very fast and the water toward the outside far away from the drain barely moving. The action of making the curve bigger actually comes from a secondary flow. The surface of the flow around a bend is a bit higher on the outside edge. It's like a bit of slosh as the bank pushes it around the curve. Well if the surface is higher on the outside, that means there is higher pressure on the outside than the inside. That pressure drives a secondary flow of water down the outside bank, across the bottom of the river toward the inside, and then back across the surface to where it started. This flow carries any eroded sediment from the outside bank to the inside. This is how you get the difference in erosion that leads to bigger meanders.

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The same explanation solves the Tea Leaf Paradox. When you stir a cup of tea with bits of tea leaves on the bottom, intuitively you may expect the leaves to all be driven to the outside edges. But no, they collect in the middle. The tea leaves are like river sediment and both are driven by secondary flow in a vortex.

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An interesting feature of this system is that there is positive feedback. Once a curve starts, it just keeps getting more and more extreme. The more curvy, the more the curve increases. Well, there's a limit to how far a river can curve because eventually the curves will intersect each other. When that happens the river will kind of short circuit and cut through that intersection instead of going all the way around the curve. That's how we get oxbow lakes. They are old river meanders that have been cut off from the main river flow.