Essence of Inviscid Shear Instability: a Point View of Vortex Dynamics

The essence of shear instability is reviewed both mathematically and physically, which extends the instability theory of a sheet vortex from the viewpoint of vortex dynamics. For this, the Kelvin--Arnol'd theorem is retrieved in linear context, i.e., the stable flow minimizes the kinetic energy
associated with vorticity. Then the mechanism of shear instability is explored by combining the mechanisms of both Kelvin--Helmholtz instability (K-H instability) and resonance of waves. The waves, which have the same phase speed with the concentrated vortex, have interactions with the vortex to trigger the instability. The physical explanation of shear instability is also sketched by extending Batchelor's theory. These results should lead to a more comprehensive understanding on shear instabilities.