Have you ever taken a walk through the rain on a warm spring day and seen that perfect puddle? You know, the one where the raindrops seem to touch down at just the right pace, causing a dance of vanishing circles?
Even before I entered the field of fluid flow research nearly 15 years ago, I was fascinated by the waves that appear after a raindrop hits a puddle.
As I became focused on the study of unstable waves in liquid sheets – geared toward mitigating undesirable waves in industrial coating and atomization processes – my fascination with puddle waves turned into an obsession. What is going on? Where does the pattern come from? Why does the impact of rain in a puddle look different than when rain falls elsewhere, like in a lake or the ocean?
It turns out that it all has to do with something called dispersion.
In the context of water waves, dispersion is the ability of waves of different wavelengths to each move at their own individual speeds. Looking down on a puddle, we see a collection of such waves moving together as one ripple in the water.
When a raindrop touches down, imagine it as a “ding” to the water surface. This ding can be idealized as a packet of waves of all different sizes. After the raindrop falls, the packet’s waves are ready to begin their new life in the puddle.
However, whether we see those waves as ripples depends on the body of water that the raindrop lands on. The number and spacing of rings that you see depends on the height of the puddle. This has been verified in some very cool ripple tank experiments, where a drop of the same velocity falls into a container with water at different depths.
Shallow puddles enable ripples, because they are much thinner than they are wide. The balance between the surface force – between the water puddle and the air above it – and the gravitational force tips in favor of surface force. This is key, since the surface force depends on the curvature of the water surface, whereas the gravitational force does not.