I was in the shower one day washing my hair, and noticed that the water falling off my hair formed perfect streams that ceased to break into droplets for quiet some distance (probably about 5-6 cm). I have kinda long hair so that greatly aided in the formation of the streams. I decided to see what would happen if the stream collided with a relatively flat perpendicular surface. I put my finger under the stream and was pleasantly surprised to see ripples upstream of the "impact". I then decided to move my finger up and noticed that these ripples became increasingly pronounced and seemingly formed a "wave". When very close to the origin of the stream (my hair) they began to turn into spherical beads. I decided to film the phenomenon to show you guys, and further below I have some theories as to what may be happening.
One theory I had was that the ripples are caused by a longitudinal wave traveling up stream, and since the compression zones are in water, they manifest as high pressure zones that cause the stream to bulge outwards as the surface tension holding the stream together is fairly flexible. The wavelength is most likely dependent (either directly or indirectly) on the speed of the falling as when I use faster flowing streams the wavelngth is a lot shorter, possible due to the faster impact. This may also be why when the impact is near the origin the stream begins to bulge more dramatically as the wavelength is a lot shorter due to the water not accelerating from free fall for as long and colliding with less force.
Another theory I had as to why the wavelength changes with finger height is that as you move down the stream since the water is moving a lot faster and the differences in speed become greater between the individual particles the water begins to decrease in density (thing spaghettification near black holes). If this does occur I don't believe it is as strong of a factor as the stream thins as it falls. This shows that rather than the spaces between the particles growing and remaining, they more likely come back together and instead manifest as the thinning of the stream.
If the cause is by both states above I may be able to formulate the density of the falling water based on the wavelength, but this is just a loose thought I have and needs more support.
I may be able to figure out if the cause is speed by looking at whether the wavelength changes as a parabolic function of finger height (as the impact speed and does, and this would possible show they're linked) but this would only be the case if impact shock waves wavelengths were linearly proportional to the impacts impulse. I would love to hear what you guys think of this idea.
My final, weaker theory I had was that the ripples are caused by the surface of the water attempting to establish a smooth transition onto the perpendicular plane, and as it curves outward, it causes a bend in the opposite way upstream which therefore causes another bend opposite to that until it smoothens out. I attempted to crudely illustrate this below.
These are lose thoughts that came to mind to support the theory, and am eager to get any feedback and share any results with you guys. If you have a completely new theory or disprove my theories please post them below, any information may help bring this question to a close.
I'm currently doing a physics extended essay, and am willing to drop my current essay for something related to this phenomenon as it seems very interesting and would be pleasure writing about.
EDIT: A friend proposed that the waves are propagated from small currents resulting from the bottles/taps shape or the hole shape. I tested this using a uniform bowl and drilled a hole in it instead of poking one to get a more uniform hole and got identical results.