Throwing a coin into a wishing well might not bring you your heart's desire, but it could cause an astonishing physical effect — a supersonic jet of air. That's if you follow the instructions of Stephan Gekle and colleagues at the University of Twente in the Netherlands and the University of Seville in Spain. They report in Physical Review Letters that when a cavity is transiently created by dropping an object into a fluid, the airflow inside it has much in common with that in a jet engine (S. Gekle et al. Phys. Rev. Lett. 104, 024501; 2010).
The authors used an experimental set-up in which a circular disc was pulled into a tank of water by a motor, breaking the liquid's surface. To visualize the airflow in the wake of the disc, they passed smoke across the surface of the water and illuminated the resulting smoke-filled cavity with laser light. A high-speed camera was used to record the smoke's movement, taking pictures at up to 15,000 frames per second. From these pictures, Gekle et al. calculated the velocity of the smoke (and so also that of the airflow) at speeds of up to 10 metres per second.
The researchers found that air is initially pulled into the expanding cavity at velocities similar to the plummeting disc's impact speed. But the walls of the cavity rapidly collapse because of water pressure, shrinking the cavity. This shrinkage reverses the direction of the airflow, ultimately causing a thin, fast air stream to surge up through the neck of the now-hourglass-shaped cavity (pictured; the diameter of the disc at the bottom of the cavity is 4 centimetres).
To calculate the air velocities that would be seen at higher speeds, Gekle et al. simulated the system mathematically. Their model incorporated equations used to describe airflow in supersonic jet engines, but with modifications that took into account the constantly changing shape of the cavities formed in their study. By combining experimental data with numerical simulations, the authors found that air can be pushed out of the cavities at supersonic speeds — even though the pressure inside the cavity is only 2% greater than atmospheric pressure.
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Mitchinson, A. Supersonic splash. Nature 463, 439 (2010). https://doi.org/10.1038/463439b