The Secret in the Sink
When a jet of water hits a flat surface, a thin, circular layer forms all around it. Why is that? These and other questions keep physicists busy to this day.
If you carefully turn on the faucet over a sink - the stream should be compact but not too powerful - you will observe an apparently water-free, almost circular area around the point of impact. It turns out to be a very thin and smooth stream that strives radially outwards. At a certain distance, it suddenly piles up much higher. From there, the water then slowly flows into the outflow.
The kitchen phenomenon is ubiquitous and yet is mostly not consciously noticed. It is a special case of a so-called hydraulic jump or alternating jump and occurs in liquids in very different forms. The circular or circular hydraulic jump has been the subject of research for years, and physicists keep finding new aspects. Under certain conditions, for example, the round shape can dissolve and become a polygon, i.e. real corners can form.
"By a movement or a leap, water can rise" (Leonardo da Vinci, 1452–1519)
The formation of the circular structure is amazing enough on its own. Even simple experiments in the sink reveal that the water circuit is extremely stable. After every disruption, no matter how strong, it forms again immediately. There are only deviations from an ideal circle due to inhomogeneities in the jet and unevenness in the surface of the sink. If you turn the tap further on or off, the radius grows or shrinks.
If you want to examine what is happening more closely, you can, for example, set up a continuous circuit in a small tub with a pump, a hose and a horizontally aligned pane of glass. This gives you an almost perfect shape. The effects of the accumulated liquid on the event can be analyzed with a height-adjustable, ring-shaped barrier at some distance from the hydraulic jump.
What is behind the phenomenon? The jet, i.e. a compact cylinder of liquid flowing in a vertical direction, shoots symmetrically in all directions after hitting the ground. In doing so, it becomes a thin disk in which the water flows away radially. On impact, its interface with the surrounding air increases enormously. In addition, a new interface is created between the liquid and the substrate. Both require a lot of energy (see "Spectrum of Science" July 2018). It can only come from the original kinetic energy of the falling water.
The interface with the air and the ground increases quadratically with the radius of the circle. The liquid layer is not only pulled apart more and more thinly with increasing distance from the point of impact of the jet, but above all its kinetic energy and thus its speed decrease rapidly. Added to this is the internal friction of the flowing liquid due to its toughness (viscosity). It too must be overcome, which is also at the expense of kinetic energy.
Water that shoots faster than its shadow
Physicists also refer to the unusually fast, radially expanding liquid as shooting: It is faster than waves and thus any form of disturbance on the surface can spread. This means that the interfaces do not form once and for all and envelop the water, as it were - like a falling drop or a soap bubble - but are continually being created anew. This requires constant energy.
Because its kinetic energy is used up as the radius increases, the shooting liquid should, to put it graphically, come to a standstill at some point. She does that too – she builds up. The higher height of the wall then compensates for its lower speed. A flow equilibrium is established in which just as much volume flows out as is supplied from the inside.
The radius of the transition depends on the impact speed and is always the same under otherwise unchanged conditions, regardless of how the surface is oriented in space. Whether the stream hits from above, below or horizontally makes little difference, as long as it is moving at the same speed. Gravity generally plays virtually no role in the circular hydraulic jump.
Where the shooting liquid comes to a standstill and piles up, the current is slowed down the most in the lower part of the layer just above the ground. Flowing liquid stumbles over it, so to speak, tilts forward and partly runs back against general direction of movement. A vortex or a tube of vortices is formed, which lies in the same radius around the center of the circle (1st vortex, illustration above). Here the water rises.
If the drain after the jump is additionally impeded by a barrier, the water continues to accumulate beyond the jump. The edge of the jump is finally flown under and tips over backwards against the general direction of flow, which has become unstable in this way. This creates a new stationary state with a second vortex. It rotates in the opposite direction and is just below the surface at the face of the wall (2nd vortex, illustration above). Subsequent liquid flows between the vortices in a slalom, thereby driving both.
The figure is not always stable. The circular shape can break up due to the smallest disturbances and form corners. These then dominate what is happening and are initially irregular and unstable. However, by carefully varying the key parameters, especially viscosity, the resulting corners can be stabilized: as regular and durable polygons, as well as other aesthetically pleasing shapes.
However, a comprehensive explanation for this is still pending. The physicists at least agree that the second, upper vortex is decisive for breaking the symmetry of the circular shape. The process in which the torus separates into individual partial flows at the edge of the jump can be seen as an analogue to the so-called Rayleigh plateau instability. The term is based on an effect that can also be observed on the faucet of a sink: the disintegration of a thin, long jet of water into individual drops. After all, a phenomenon rarely comes alone.
