Instability of circular array of slender helical vortices

抄録

For the first time stability of a multitude (couple, triplet, quad, etc) of the helical vortices with and without additional rotation from central vortex and axial translation has been investigated analytically. In practice an existence of a couple or triplet has been observed in different vortex flows (e.g. in tornado cores; after vortex breakdown and in vortex chambers; as a model of the vortex couplings in turbulent flows etc.). A quad (and more) is absolutely unstable structure. In contrast to this the systems with central vortex (wakes behind propellers and turbines) are stable. All previous studies based on the stability analysis of point vortex systems conflicted with the data but all of the observations are in accord with the stability analysis of the helical vortex structures.