Wave Motion in Circular Jets

A fluid jet in a nonviscous incompressible medium is capable of sustaining a number of vibrational modes in analogy with electromagnetic waves in a wave guide. This paper enumerates and classifies modes that would be excited by small disturbances at the orifice of a circular jet. By means of perturbation theory these modes are shown to be of the form Φ = [AIn(kr) + BKn(kr)] exp[−inθ−ikz+iωt], where In and Kn are modified Bessel functions and Φ is the velocity potential. Physically these represent waves propagating down the jet which increase in amplitude from the source of the disturbance until jet rupture occurs and turbulence results.