Physicists Discover What Happens Inside a Stable Vortex

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Large vortices with characteristic spiral arms are often observed in the atmosphere and the ocean. Physicists from HSE University have explained how these structures form and why they retain their shape. The researchers found that velocities at points located along the same vortex arc remain correlated even over long distances. At the same time, this correlation weakens rapidly with increasing distance from the vortex centre. These differences help explain the formation of spiral arms and may improve models of atmospheric and oceanic currents. The findings have been published in Physical Review Fluids.

Turbulent flow is the movement of a liquid or gas, which is characterised by vortices, intense mixing, and sudden changes in velocity. It is impossible to trace the movement of each particle in such a stream, so researchers describe it through averaged characteristics. For example, using the paired correlation function, it is possible to understand how the fluid velocities are related at two flow points.

For fully developed turbulence, in which all directions are equivalent and there is no rotation, such correlations have already been studied in considerable detail. In a three-dimensional flow, the resulting vortices break up into smaller ones, and at large distances the velocities are practically independent of one another. In a two-dimensional flow, by contrast, vortices tend to merge into larger structures, and the correlations between velocities decay much more slowly with distance. 

In a rapidly rotating three-dimensional fluid, the structure of the flow changes: the mean flow, represented by a large vortex, becomes flatter, while small fluctuations within it retain a complex three-dimensional character. It is the interaction of these fluctuations that determines the statistical properties of the flow inside the vortex.

In their new paper, Prof. Sergey Vergeles and Associate Professor Leon Ogorodnikov from the Landau Institute for Theoretical Physics and the International Laboratory for Condensed Matter Physics at HSE University studied a rapidly rotating three-dimensional fluid in which a stable coherent vortex forms—a massive swirling flow that can arise in the ocean and atmosphere. In the atmosphere, such vortex structures are clearly visible in cyclones and anticyclones, where clouds gather in spiral arms, forming dense, extended regions. The authors investigated how velocity correlations within such a vortex behave both locally and at a distance. The researchers considered three components of velocity: radial (motion toward or away from the vortex axis), azimuthal (circular motion around the vortex axis), and vertical (motion along the vortex axis). 

It was found that correlations between velocities persist over long distances and decay slowly as the distance increases, but in different ways depending on direction: slower (logarithmically) along the circumference of the vortex, somewhat faster along its axis, and even faster (power-like) in radial direction. This effect arises from the spatial inhomogeneity of the medium’s rotation, in which fluid elements located at different distances from the rotation axis move with different angular velocities and therefore complete full rotations in different amounts of time. This slow decay of velocity correlations in the azimuthal direction, compared with the radial direction, is clearly manifested in spiral arms that are elongated along the direction of rotation of the fluid and compressed in the transverse direction. Similar spiral structures are observed in galaxies. Although these systems are governed by different physical processes, it is the inhomogeneous (differential) rotation that leads to the formation of arms of a similar shape.  

The authors also found that correlations between identical velocity components are largely independent of the specific way energy is injected into the system, whereas correlations between different components are sensitive to it.

Leon Ogorodnikov

'The long-range correlations between identical velocity components are largely independent of the statistical properties of the forcing that supplies energy to the system. In contrast, the cross-correlations between the radial and azimuthal velocity components behave differently: they are weaker, decay more rapidly with distance, and show a strong dependence on the forcing correlation function,' comments one of the study authors, Leon Ogorodnikov, Junior Research Fellow at HSE University's Laboratory for Condensed Matter Physics and the Landau Institute for Theoretical Physics.

The study findings can help better understand the internal structure of large coherent vortices that form in oceanic and atmospheric currents on Earth and other planets.