The work stands apart: there is almost nothing nearby, the closest neighbor is at a distance of 0.54, and zero works are adjacent. Surrounding studies include vortices in quantum fog, electronic vortices on nanowires, superfluid vortices with memory, as well as a solar heat pump and slow Rossby waves. These neighbors investigate vortex structures and waves in different media, but none have provided a theory linking the profile of a geostrophic vortex to the absorption of inertial waves in a turbulent rotating fluid. This work fills that gap, building on the authors' own experiments with excitation at vertical walls.
The authors consider an incompressible fluid in a box of height H, rotating at angular velocity Ω. The total velocity field is decomposed into a geostrophic component U(t; x, y), depending only on horizontal coordinates, and a fast part u describing an ensemble of inertial waves. In the limit of rapid rotation, nonlinear wave interactions are neglected, and the dynamics of u obey the linearized Navier–Stokes equation. Waves are assumed to be excited at the periphery and propagate inward. For an axisymmetric vortex, the Reynolds equation reduces to an ordinary differential equation for the angular velocity W(r). The key contribution to the Reynolds stress comes from waves absorbed in the critical layer, where the Doppler-shifted frequency vanishes. The equation is solved numerically, with parameters fitted to experimental profiles.
The theory reproduces the measured angular velocity profiles W(r) for cyclones at seven rotation speeds from 1.13 to 4.52 s⁻¹. The fitting parameters are the bottom friction coefficient κ and the characteristic wavenumber $k_f$. Both increase with Ω. At fast rotation (Ω > 2.5 s⁻¹), the profile W(r) exhibits a power-law decay, while at slow rotation (Ω = 1.1–2.3 s⁻¹) a region of exponential decay is visible. The intermediate asymptotics of the shear velocity Σ(r) is exponential for all Ω: Σ(r) ∝ exp(−κr). The computed energy injection rate ε and the experimentally measured $ε_{exp}$ = 2αE agree with a mean ratio ε/$ε_{exp}$ ≈ 1.4, confirming the model's plausibility.
Unlike neighbors who study vortices in quantum or electronic systems, this work provides a theory for classical rotating turbulence. It is the first to link the profile of a geostrophic vortex to the absorption of inertial waves, rather than to volumetric forcing as in previous models. This is not just statistics but a deterministic description of the vortex structure, validated against the authors' own experiments with smooth horizontal boundaries.
The topic could evolve toward accounting for nonlinear wave interactions, which become important at slow rotation. This would allow describing anticyclones observed in the same experiments, where the profile W(r) changes sign. Another direction is generalizing to anisotropic forcing or to vortices with non-axisymmetric shapes.
The results apply to geophysical flows: ocean eddies and atmospheric cyclones, where rotation and turbulence coexist. They are also useful for laboratory experiments on rotating turbulence.
The next step is to build a theory that includes nonlinear wave interactions to describe the anticyclone regime. It is also worth testing the model on other forcing configurations and at different Rossby numbers.
For the hydrodynamics of rotating fluids, the role of nonlinear wave interactions in shaping large-scale structures remains an open question. This work delineates the boundary of validity of the linear approximation and indicates where a theory of weak wave turbulence is needed.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors built a theory linking the radial profile of a geostrophic vortex to the absorption of short-wavelength inertial waves in the strong-rotation limit. By solving the axisymmetric Reynolds equation with a key contribution from the critical layer, they reproduced the experimental angular velocity profiles at various rotation rates and matched the calculated pumping power to the measurements.
Where its strength is
The work provides a deterministic description of the vortex structure, grounded in a specific wave absorption mechanism, and confirms it with the authors' own experiments using smooth boundaries. This lays the groundwork for further study of wave-vortex interaction in classical rotating turbulence.
Where it could go next
Worth trying
Why this may matter
This link between wave pumping and vortex structure could prove useful for understanding energy transfer in geophysical and astrophysical flows, where rotation and waves play a key role.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.56, against a usual 0.64. It looks like few have drilled nearby.
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.