Why does a river meander instead of running straight?

Because any tiny bend feeds itself. Water on the outside of a curve travels faster and erodes the bank; on the inside it slows and drops sediment. So the outside is cut away and the inside builds up, and the bend gets bigger - which makes the effect stronger, and so on. A perfectly straight channel is unstable; the smallest irregularity grows.

It goes further than curving. As bends tighten, the neck between two of them narrows until a flood cuts straight across, abandoning the loop as an oxbow lake. The whole river is therefore migrating sideways across its floodplain over centuries, which is why old maps of the Mississippi look like marbled paper and why river boundaries between countries generate lawsuits.

There is a surprising regularity underneath it. Meander wavelength scales with channel width by roughly a constant factor across rivers of wildly different sizes, from a trickle in sand to the Amazon, and the same pattern appears in meltwater channels on ice sheets and in the Gulf Stream, which has no banks at all.