A Whirlpool That Drinks Waves ✛ ✎

Original: "Maintenance of a columnar vortex by inertial waves in rotational turbulence"

· Nikolay A. Ivchenko, Sergey S. Vergeles, Daniil D. Tumachev, Sergey V. Filatov

arXiv:2609.06158v1 · 2026-09-05 · arXiv non-exclusive · independent analysis · 1 min

How turbulent waves sustain a long-lived vortex in a rotating fluid.

Water in a tank spins fast, and a column appears that lives long even though everything around it is churning. This column is a vortex, and it doesn't disappear because waves feed it.

Waves are born at the tank walls and travel inward, like ripples across a pond. When a wave enters the vortex, it gives up its energy. This happens in a special place where the wave's speed matches the rotation speed of the water. There, the wave sort of melts, and its energy transfers to the vortex.

The scientists built a theory that predicts how fast the water spins at different points in the vortex. They compared the calculations with experiments, and they matched.

Now it's clear why ocean eddies and atmospheric cyclones live so long. They, too, can drink waves that come from far away.

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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.

αU + \frac{1}{r^2} \partial_r (r^2 \Pi_{r\phi} - \nu r^2 \Sigma) = 0

The balance between bottom friction, Reynolds stress, and viscosity determines the velocity profile

\tilde{\omega} = \sqrt{2\tilde{\Omega}(2\tilde{\Omega}+\Sigma)} \frac{s k_z}{\sqrt{k_r^2 + k_\perp^2}}

The wave frequency depends on the local rotation and shear, leading to critical layers

\rho = \frac{2\Omega q}{2\tilde{\Omega}(2\tilde{\Omega}+rW')} \frac{|mW'|}{k|\omega|} \ll 1

When ρ is small, the wave is efficiently absorbed in the critical layer, and reflection can be neglected

Concepts

vorticity turbulence standing wave law of conservation of angular momentum coronal heating mechanism vortex lattice gravitational waves superfluid vortex turbulent mixing continuous gravitational wave law of conservation of momentum principle of constancy of the speed of light ocean current flow virial theorem Kelvin-Helmholtz instability rotational energy fluid dynamics in porous media inertia pulsar wind nebula

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A Whirlpool That Drinks Waves ✛ ✎