Concentration of vorticity due to selective decay in doubly periodic vortices and a vortex pair

Strong vortices like tornadoes, typhoons, and tropical cyclones are often created in geophysical flows. It is important to understand the mechanism for the creation of these strong vortices. Recently, we found a purely hydrodynamic mechanism for the concentration of vorticity: it is due to selective decay in which circulation decays faster than angular momentum and energy. In this paper, two problems are investigated by direct numerical simulation to seek universality of this mechanism: doubly periodic vortices disturbed by an unstable eigenmode and a vortex pair disturbed by localized disturbances. In the former case, concentration of vorticity occurs when the wavenumber of the eigenmode is large, while it does not occur for small wavenumbers. For small wavenumbers the disturbances grow to a large amplitude eventually destroying the base flow. For large wavenumber, on the other hand, the growth of the disturbances saturates before destroying the base flow. Selective decay of inviscid invariants is shown to be responsible for the concentration of vorticity as in the previous study. In the case of a vortex pair disturbed by localized disturbances concentration of vorticity occurs twice: the first concentration is not related to selective decay; however, the second weak concentration is most likely due to selective decay.