Propagation and growth of surface waves on a supersonic fluid jet

The unstable surface waves that propagate along a jet of cylindrical cross section are investigated in the vortex sheet approximation in static pressure balance with an external medium. Attention is restricted to the helical wave mode and a representative sample of the fluting wave modes that are harmonics of the helical wave mode. These wave modes share common properties. A simple expression for the maximally unstable wavelength of these wave modes is found from the numerical results. The effect of a changing wave phase velocity on the growth of a wave is investigated. A change in phase velocity of growing waves results because conditions in a jet change in response to a changing external medium. This can be stabilizing or destabilizing, and the characteristic wavelength of a wave mode can be considerably different from the instantaneous maximally growing wavelength, depending on the way in which the jet Mach number and jet-to-external-medium density ratio vary.