When one turns on the tap in the kitchen, a circle is observable in the water flowing in the sink. The circle is the boundary between laminar and turbulent flow of the water (maybe this is the wrong terminology?). On the inside the height of the water is lower than on the outside. I'm sure that you have seen it many times, if not you can try it out yourself.
I found out by experiment that the effect is most likely independent of the curvature of the sink, as it works in strongly curved bathroom sinks as well as in flat kitchen sinks.
Why is there a circle, why not a gradual change and what is happening qualitatively and/or quantitatively in this system?
As I have not found a satisfying answer to this problem yet, every time I turn on a tap, I am reminded of my own ignorance. It is really annoying.
Best Answer
You are observing a hydraulic jump.
The Wikipedia article is very good, so I won't try to out-do it.
In brief summary, when the water starts running out from the place where it hits the sink, the same flux is spread out over a larger and larger circumference as you move out. This means the flow gets shallower and moves more slowly as you move further out.
If a wave propagates in this flow, its wave speed depends on the height of the water. Its speed relative to the flow also depends on the flow speed. So the propagation of wave changes as we move further out as the flow underneath the wave changes.
The wave itself changes the height of the water - the water is deep at the peak of the wave and shallow at a trough. Different parts of the wave moves at different speeds. This is clearly a non-linear phenomenon. Similar to waves crashing at the beach, eventually the propagating wave crashes over on itself. This causes a "hydraulic jump". The main effects are
The physics of water in your sink is not very easy - since the flow is so shallow, surface tension has considerable importance. You can learn more details in the Wikipedia article linked above.