Water in a tank spins at nearly four revolutions per second, and, as if by magic, a column the size of a dinner table emerges. The vortex lives for dozens of rotations, even though everything around it churns and trembles. Where does such stability come from?
The secret is that the vortex is not isolated. It is fed by waves that are born at the tank walls and travel inward, like ripples across a pond. These waves are called inertial because they are driven by the Coriolis force, the same one that swirls water down a drain. The waves carry energy, and the vortex drinks it in like a well absorbing rainwater.
To test this picture, physicists built a theory. They split the fluid motion into the slow rotation of the vortex and fast waves, then reduced the complex equations to a single simple one: how the rotation speed changes from the vortex center to its edge. Plugging in parameters from experiments, they obtained curves that almost exactly matched the measurements.
Remarkably, the vortex is not simply "smeared out" by turbulence; it forms a sharp velocity profile. At the center, it rotates almost like a solid body, and toward the edge the speed drops. For fast rotation, the decay follows a power law; for slow rotation, it is exponential. It is as if the well had different wall shapes depending on the strength of the rain.
The same logic applies to the ocean and the atmosphere. Oceanic eddies and atmospheric cyclones live for weeks, even though turbulence rages around them. Perhaps they, too, are fed by waves arriving from afar. A theory tested in a water tank gives us a tool to peer into the heart of a hurricane.
The characteristic wavenumber $k_f$ in the experiments is on the order of 1 cm⁻¹, meaning a wavelength of about a centimeter, while the vortex has a radius of about 40 cm. The vortex lives for tens of its own rotation periods, even though it is fed by waves that are fully absorbed within fractions of a second.