It makes waves. Even without friction, the waves spread out and die away. Things like solitons show up in lots of physical theories, called various solitions, kinks, hedgehogs, monopoles and lumps. For many lumps, you can prove they won't disperse by using things like the winding number. A flat lake, after a wave has dispersed, has a winding number of zero.
Lumps have non-zero winding number.
Therefore you can only get from a lump to a flat lake by a discontinuous transformation. Nature doesn't like discontinuities. Winding number also shows up in pattern formation. If conditions are just right, different parts of the solution are at different phases in the cycle, and the mixture spontaneously forms spiral waves. The trick is that spirals can point in two senses, clockwise and counter-clockwise, and that these two senses give winding numbers of opposite sign.