I was helping my three year old brush his teeth when he pointed out to me that the water wrinkles when he puts his finger in it. He showed me and sure enough, it wrinkled. Fortunately, he did not ask me why. I had to do some research. I tried it as seen above.
With a little help from MIT and a dumbed down summary at the end, I can now answer confidently when asked why the water wrinkles.
The full lecture can be found here. If you are into the equations that make it work, check it out. They also have some cool pictures.
The Plateau-Rayleigh Instability
The principle at play is known as the The Plateau-Rayleigh Instability. Water falling in a jet or stream (like it does from your kitchen tap) becomes unstable after falling for a certain distance.
Says MIT using real big words:
When the volume flux exiting the tap is such that the falling stream has a diameter of 2–3mm, obstructing the stream with a finger at a distance of several centimeters from the tap gives rise to a stationary field of varicose capillary waves upstream of the finger
As the perturbations increase, the wavelengths of the disturbances exceed the circumference of the falling water jet making it wrinkle. Eventually, the water will break into droplets. Most anyone has noticed this with a garden hose or in their own kitchen sink. Placing your finger an inch or two under a small stream from a kitchen sink will allow some stationary capillary waves to form. Or as my three year old said, it makes the water wrinkle. Mystery solved.
Additional experiment to try yourself
If you put soap on your finger, the wrinkles will form a certain distance from the finger instead of directly above your finger. Neat.