ON THE EQUILIBRIUM AND STABILITY OF A ROW OF POINT VORTICES

The equilibrium and stability of a single row of equidistantly spaced identical point vortices is a classical problem in vortex dynamics, wh ich has been addressed by several investigators in different ways for at least a century. Aspects of the history and the essence of these tr eatments are traced, stating some in more accessible form, and pointin g out interesting and apparently new connections between them. For exa mple, it is shown that the stability problem for vortices in an infini te row and the stability problem for vortices arranged in a regular po lygon are solved by the same eigenvalue problem for a certain symmetri c matrix. This result also provides a more systematic enumeration of t he basic instability modes. The less familiar theory of equilibria of a finite number of vortices situated on a line is also recalled.