I've observed this behavior many times. When it rains, the rainwater will form vertical channels along a glass window. The flow of water is mostly confined within these vertical channels and the channels are (more or less) stable.
But sometimes - and I suspect this happens when the flow intensity in one of the channels increases - the channel will switch from a vertical configuration into a zig-zag configuration. The zig-zag is composed of short segments running horizontally that are connected by semicircular (vertical) segments. The zig-zag is unstable and lasts only for 0.1 second or so. Then the channel reverts to its vertical configuration.
I have made photographs of this behavior but I cannot find them now.
I have seen similar patterns in the book "The self made tapestry" by Philip Ball, page 145. This shows growth instabilities in glass cracks. Is says "at higher speeds the crack becomes oscilatorry with a constant wavelength". This is what I see in the water flow. It feels counterintuitive.
There must be a good explanation for this behavior. Can you point me to it?
EDIT Here is a video .