A note on the stability of a cylindrical vortex sheet

Abstract

An inconsistency in a previous stability analysis of a cylindrical vortex sheet is resolved. It is found that disturbances with azimuthal wavenumbers m = 1 and 2 are stable, whereas previously the stability of these modes was uncertain. It has been hypothesized that the multiple-vortex phenomenon is initiated by such an instability (Ward 1972). Since double vortices (m = 2) arise, we are led to consider a central downdraft surrounded by a uniform updraft; for a non-zero vertical wavenumber γ, the modes m = 1 and 2 are destabilized. Our theory is supported by the observation that double vortices tend to form as intertwining spirals (i.e. they have vertical structure).