Evolution of a barotropic shear layer into elliptical vortices

TL;DR

This paper investigates how a piecewise linear shear layer develops into elliptical vortices through Kelvin-Helmholtz instability, revealing the role of vorticity wave interactions and explaining phenomena in geophysical and astrophysical flows.

Contribution

It demonstrates that the interaction of counter-propagating vorticity waves causes elliptical vortex formation, providing new insights into vortex dynamics in various natural flows.

Findings

Elliptical vortices form from shear layers via vorticity wave interactions.

The study explains the oscillation, rotation, and nutation of elliptical vortices.

Results relate to vortex phenomena in geophysical and astrophysical contexts.

Abstract

When a barotropic shear layer becomes unstable, it produces the well known Kelvin-Helmholtz instability (KH). The non-linear manifestation of KH is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KH characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counter-propagating vorticity waves is solely responsible for this KH formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides possible explanation behind the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g. meddies, Stratospheric polar vortices, Jovian vortices, Neptune's Great Dark Spot and coherent vortices in the wind belts of Uranus.