Enlarge /. A red dune racing around an underwater track.
Sand dunes are incredible. They sing, they move, they organize themselves into regular structures – and then these structures can fall apart. Dunes can collide and merge into a single dune, and a single dune can break up into multiple dunes. We all know pictures of dune fields in the desert, but you may not notice that the sand waves on the seabed are also dunes – just on a different scale. To test our understanding of sand dune models, physicists played with underwater sand castles. The result is that the models are fine but need work.
Dunes are not just a creation of sand; They are the result of a combined effort between free-flowing sand and a liquid (water or air) that moves it. Understanding this dynamic includes a combination of modeling and measurement.
However, modeling is … a challenge. A single dune contains too many particles to create a particle model. Researchers have therefore found an abbreviation: They model dunes as autonomous blobs that can take care of the desert. As the dunes move and collide, they exchange mass. After all, all dunes have the same mass and move at the same speed, which leads to regular structures as we observe them in dune fields and stream beds.
So the model is pretty good and it's not like it was pulled out of thin air. The properties of the model are based on observations. But that doesn't mean it's right.
To uncover the dynamics of the dune movement, a group of researchers did a very cool experiment: they created a pair of dunes in a donut-shaped water tank that is about a quarter turn apart. Then they stirred the water vigorously enough to create a very turbulent flow and watched what happened.
If the model were correct, the two dunes would move at the same speed. But for this to happen, they had to exchange mass until the two dunes were the same size.
Everything got excited
However, this is not the case. Instead, the downstream dune would happily take off and move at a speed of 16 meters per hour, while the upstream dune would fight at a slow speed of 12 meters per hour. As the downstream dune continued to advance, it slowed. It would take so long for the two dunes to face each other. Then they would move at the same speed. And at that point, it no longer made sense to label one thing before the other – they were balanced.
At no point in this process do the dunes exchange significant mass. Quite simply, as long as the dunes exceed a certain size, they are always in a balanced position, although the speed and other details vary.
The key, according to the researchers, is turbulence. The flow created by the experiment is very turbulent (as it would be in nature), and the shape of the dunes also creates additional turbulence. The video analysis shows that the upstream dune experiences a large particle movement that is driven by turbulence, while the downstream dune appears to be sitting in a relatively calm area. If the dunes move at the same speed, their particle movement is also roughly the same.
Even if the dunes vary considerably in size, the turbulence appears to prevent them from colliding. The dunes reach the same speed before they reach an angle of 180 degrees with large mass differences. The balance is not stable on longer timescales. The upstream dune is slowly losing mass to the downstream dune, although this happens without the dunes getting any closer.
However, we should remember that this work was done in water. The mass balance between the liquid medium and the sand also plays a role in the dynamics of the dunes. This balance is significantly different in the air.
However, this work shows some discoveries. First, the autonomous model is not bad, especially with long time scales. The model predicts the changing mass balance and the possible speed balance. However, the model does not predict collision avoidance. In actual experiments, the dunes do not collide, which tells us something about what is wrong with the model.
But nature tells us something else: dunes sometimes collide, but there are also signs of repulsion between dunes. Overall, I think this tells us model builders just have to grit their teeth and include turbulence. Better them than me.
Physical Review Letters, 2020, DOI: 10.1103 / PhysRevLett.124.054501 (About DOIs)