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.Comment: 7 pages, 4 figures, Accepted in Physical Review