Columnar vortices in rotating fluids — the elongated vortex structures maintained by Coriolis force — are ubiquitous in geophysical and astrophysical flows. Their stability has been studied for decades, primarily through energy methods and spectral analysis of linearized operators. But the asymptotic linear stability for the 3D axisymmetric Euler equations has remained unresolved.
The paper establishes this stability rigorously using a distorted Fourier basis adapted to the vortex structure. The standard Fourier basis diagonalizes the free Euler operator, but the vortex introduces a background flow that couples modes in a way that makes direct spectral analysis intractable. The distorted basis absorbs these couplings — it is constructed to respect the vortex geometry rather than the ambient geometry.
The Coriolis force plays a dual role. It maintains the columnar structure in the first place, preventing the three-dimensional spreading that would destroy the vortex. But it also stabilizes the vortex against perturbations by enforcing a rotational constraint that limits the growth of unstable modes. The force that creates the structure also protects it.
This is not automatic — rotating flows can be unstable (centrifugal instability, inertial wave resonances). The stability here is asymptotic: perturbations decay in time, returning the flow to the columnar vortex state. The proof works in the inviscid (Euler) setting, meaning the stabilization comes from the dynamics itself, not from viscous damping.
The distorted Fourier approach may be more broadly applicable to stability problems where a background structure couples standard spectral modes. The technique transforms an intractable coupling problem into a diagonal one by building the background geometry into the basis functions.
Coriolis force both creates and stabilizes columnar vortices — the rotational constraint that maintains the structure also suppresses perturbation growth, providing asymptotic stability even without viscous dissipation.