River as a chaotic system

As a physicist I love to observe rivers and catch the elements of chaotic systems. In the heat summer, a river runs slowly. Its surface appears calm and seren. Where it encounters a rock, the water parts and flows smoothly past. The rocks or other obstacles are the bifurcation points that change character of the motion.

But in spring, after heavy rains, the river has a different character. In these circumstances, one part of the river runs slightly faster than a neighboring region and acts to speed up the stream around it, which, in turn exerts a drag on the faster flow. Each part of the river acts as a perturbing effect on all the other parts. The effects of these perturbations are constantly being fed back into each other. The result is a chaotic motion in which different regions are moving at different speeds.

As the fast - flowing river approaches the rock, it swirls and turns back on itself. Behind the rock, a vortex is born and persists as a highly stable form. The river is demonstrating all the characteristics of chaos. Its behavior is highly complex, including random, unpredictable flows, eddies, and stable vortices. These complex structures in chaos language are attractors.

As the river's speed picks up further, the vortices unravel into local regions of choppy, swirling water. Finally, with the water flowing rapidly, the region behind the rock seems to have lost all order, and true turbulence has set in. The motion of each tiny element of the water appears to be random.

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